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INDUCTIVE LOGIC 



INDUCTIVE LOGIC 



By JOHN GEIER HIBBEN, Ph.D. 

ASSISTANT PROFESSOR OF LOGIC IN PRINCETON UNIVERSITY 



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NEW YORK 

CHARLES SCRIBNER'S SONS 

1896 



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COPYRIGHT, 1896, BY 
CHARLES SCRIBNER'S SONS 



Nortoaoti 5f«as 

J. S. Cushing & Co. — Berwick & Smith. 
Norwood Mass. U.S.A. 



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CONTENTS 



Chap. I. — The Nature of Inference ... 1 

Psychological and Logical Elements in Inference, page 1 ; 
Objective and Subjective Necessity, 4 ; Data of Presen- 
tation, 5 ; System as Ground of Inference, 6 ; The Im- 
plicit and Explicit, 11 ; Inference mediated through 
the Universal, 12 ; Conceptual Processes, 13 ; Explana- 
tion, 14. 

Chap. II. — Induction and Deduction ... 16 

Various Opinions concerning their Relative Importance, 
page 16 ; Regarded as Different Phases of One and 
the Same Process, 17 ; Their Relation to the Ground 
of Inference regarded as a System, 17 ; Their Relation 
to the Universal, 18 ; Difference between Truth and 
Fact, 19 ; Mutual Dependence of Induction and De- 
duction, 20. 

Chap. III. — The Essentials of Induction . . 24 

The Inductive Hazard, page 24 ; Basal Postulate of Induc- 
tion, 25 ; Its Epistemelogical Nature, 26 ; Induction 
regarded as an Inverse Process, 27 ; Law and Rule, 30 ; 
Law in Terms of an Hypothetical Universal, 31 ; Induc- 
tion in the Conduct of Human Affairs, 32 ; The Scien- 
tific Spirit, 33. 

Chap. IV. — Types of Inductive Inference . . 34 

The Method of Enumeration, page 35 : a. Perfect Induc- 
tion, 36 ; b. Incomplete Enumeration, 37 ; c. Proba- 

v 



vi CONTENTS 

bility, 38 ; The Method of Analogy, 39 ; The Method 
of Scientific Analysis, or Causal Determination, 40 ; 
The Causal Postulate underlying All the Methods, 43 ; 
Relation of Mental Habit to Choice of Method, 47; 
Generalization, 48. 

Chap. V. — Causation 50 

Logical Significance of the Causal Concept, page 50 ; Its 
Phenomenal Significance — The Conservation of En- 
ergy, 51 ; Its Philosophical Significance, 53 ; Its Logical 
Significance, 54 ; Its Epistemelogical Ground, 58 ; Pop- 
ular and Scientific Idea of Cause, 58 ; Causal Analysis, 
60 ; Limitations of Knowledge, 62. 

Chap. VI. — Causal Analysis and Determination 64 

Sequence, page 64; Concurrence, 66; Co-existence, 66; 
Vital Growth and Development, 68 ; Collocation, 68 ; 
Different Modes of Transfer of Energy, 71 ; Quantita- 
tive Determination, 72 ; Observation and Experiment, 
73 ; Negative Determination, 78 ; Pseudo-causal Con- 
nection, 82. 

Chap. VII. — Mill's Inductive Methods — The Method 
op Agreement ....... 84 

The Five Methods, page 84 ; The Method of Agreement, 
86 ; Symbolic Representation, 87 ; Variation of In- 
stances, 90 ; The Method of Agreement and Observa- 
tion, 91 ; Relation to Simple Enumeration, 91 ; Se- 
quence and Co-existence, 92 ; Defects of this Method, 
93 ; Its Chief Function, that of Suggestion, 96 ; Illus- 
trations, 97. 

Chap. VIII. — The Method of Difference . . 101 

Relation to Method of Agreement, page 101 ; Its Charac- 
teristics, 101 ; Symbolic Representation, 103 ; Similar 



CONTENTS Vll 

to Negative Determination, 104 ; Relation to the The- 
ory of Combinations, 105 ; Criticisms of this Method, 
106; Practical Difficulties, 109; Illustrations, 113; 
Blind Experiments, 115. 

Chai». IX. — The Joint Method of Agreement and 
Difference ........ 117 

Relation to Method of Difference, page 117 ; Symbolic Rep- 
resentation, 118; Difficulty of Elimination, 121; Illus- 
trations, 124 ; Advantage of this Method over the 
Simple Method of Agreement, 128. 

Chap. X. — The Method of Concomitant Variations 130 

Its Characteristics, page 130; Its Symbolic Representation, 
131 ; Quantitative Determination, 131 ; Graphic Repre- 
sentation, 133 ; Psychological Impressions, 133 ; Illus- 
trations, 134; The Comprehension of the Intensity of 
Unknown Forces facilitated by this Method, 141 ; Lim- 
itations of this Method, 142. 

Chap. XL — The Method of Residues . . . 146 

A Method of Elimination, page 146 ; Symbolic Representa- 
tion, 146 ; A Deductive Method, 147 ; The Complexity 
of the Residual Element, 148 ; Illustrations, 149 ; Re- 
sidual Error in Experiments, 153 ; The Mental Habit 
of inspecting All Remainders, 154. 

Chap. XII. — Verification and Prediction . . 156 

The Inducto-deductive Method, page 156 ; Verification, 157 ; 
Prediction, 159 ; Illustrations, 160 ; Bacon's Anticipa- 
tions of Nature, 163 ; Scientific Thought, 164 ; Indirect 
Method of Prediction, 166 ; Exception Phenomena, 170 ; 
Generalization, 171 ; Mathematical Method, 172. 



Viii CONTENTS 



Chap. XIII. — Hypothesis 174 

Hypothesis, as Preliminary to Experiment, page 174 ; Hy- 
pothesis, in place of Experiment, 176 ; Illustrations, 
177 ; Function of the Imagination in Hypothesis, 184 ; 
Analysis and Synthesis, 186 ; Eequirements of a Legit- 
imate Hypothesis, 187 ; Postulate and Hypothesis, 189 ; 
Fictions, 196 ; Suggestions through Failure of Hypoth- 
eses, 197 ; Consilience of Inductions, 198 ; Experimen- 
tum Crucis, 199 ; Whewell and Mill, 201. 

Chap. XIV.— Analogy 204 

Analogy as Suggestive of Inductive Inquiry, page 204 ; 
Analogy in Generalization, 204 ; Formation of Con- 
cepts and Analogy, 205 ; Natural Kinds, 205 ; Classifi- 
cation, 207 ; Teleology, 208 ; False Analogies, 220. 

Chap. XV. — Probability ...... 226 

Complexity of the Causal-nexus, page 226 ; Relation to 
Enumerative Induction, 228 ; Calculation of the Proba- 
bility of a Particular Event, 230 ; Adverbial Probabil- 
ity, 232 ; Estimate of Aggregates, 231 ; Chance and 
Coincidence, 243 ; Circumstantial Evidence, 247 ; Rela- 
tion to the Method of Residues, 251. 

Chap. XVI. — Empirical Laws .... 252 

Three Classes of Laws of Varying Degree of Probability, 
page 252 ; Empirical Law as Expression of Causal 
Relation in Process of Determination, 253; Colloca- 
tions giving Rise to Empirical Laws, 254 ; Generaliza- 
tions expressing an Aggregate of Qualities in the Same 
Individual, 256 ; Probability and Empirical Laws, 258 ; 
The Method of Agreement, 259 ; The Empirical Nature 
of the Causal Relation, 260. 



CONTENTS ix 



Chap. XVII. —Fallacies 262 

Of Perception, page 263 : a. Failure to comprehend the 
Entire Field of Vision, 263 ; b. Failure to concentrate 
Attention, 265 ; c. Errors due to Apperceptive Projec- 
tion, 266 ; Of Judgment, 266 : a. False Associations, 
267 ; b. Emotional Perturbation, 267 ; c. General Frail- 
ties of Human Nature, Bacon's Idols, 269; Of Imagi- 
nation, 271 ; Of the Conceptual Processes, 275 : a. Hasty 
Generalization, 276 ; b. Interpolation in a Series, 277 ; 
c. Provincialisms, 278 ; d. False Analogies, 278 ; e. In- 
correct Classification, 279 ; Psychological Character of 
these Fallacies, 279. 

Chap. XVIII. — The Inductive Methods as applied to 
the Various Sciences ..... 281 

Nature of Method will vary with Nature of the Phenomena, 
page 281 ; Complication of the Doctrine of the Conser- 
vation of Energy, 287 ; The Phenomena of One Science 
to be interpreted in the Light of the Results of Another 
Science, 290 ; Growing Tendency to supplement Deduc- 
tive Method by Inductive, 292. 

Chap. XIX. — Historical Sketch or Induction . 297 

Socrates, 297 ; Plato, 297 ; Aristotle, 298 ; Roger Bacon, 
300 ; Leonardo da Vinci, 301 ; Telesius, 302 ; Campa- 
nella, 303 ; C?esalpinus, Copernicus, Gilbert, Kepler, 
Brah<§, Galileo, 304 ; Francis Bacon, 304 ; Locke, 307 ; 
Newton, 307 ; Herschel, 308; Whewell, 310 ; Mill, 311. 

Chap. XX. — Logical Exercises .... 313 



PREFACE 

It has been my aim, in the following pages, to 
present the essential features of inductive logic, 
in the hope that this work may prove a fitting 
supplement to the elementary courses in formal or 
deductive logic. The impression is too often left 
in the minds of those who have pursued the 
study of deductive logic exclusively that the for- 
mal laws of the syllogism constitute the entire 
body of logical doctrine, and that reasoning con- 
sists solely in drawing conclusions from given 
premises. There is danger here lest reasoning 
become associated with an artificial procedure 
that seems to find its proper sphere in the solu- 
tion of verbal quibbles and logical puzzles. In 
the actual experiences of life, we do not find 
our premises ready made. They are the result 
of wide observation and patient investigation and 
experiment. We challenge premises that are 
given, and Aveigh their significance. We meet 
particular facts before we do the general laws. 



xii PREFACE 

The former must be tested and interpreted, before 
we can rise to the general laws which underlie 
them, and which may stand as the major prem- 
ises of our syllogisms. Thus within the very 
sphere of deduction itself there naturally opens 
a wide field for inductive inquiry. Therefore I 
have emphasized the necessity of a thorough 
knowledge of the principles of inductive logic 
in order to comprehend the material as well as 
the formal elements in inference, and without 
which no firm grasp of the general process of 
reasoning is possible. I have also insisted upon 
regarding induction and deduction as mutually 
dependent ; not as separate modes of inference, 
but rather as different phases of one and the 
same logical procedure. 

I have endeavored, also, to indicate in some 
measure at least, the salient characteristics of 
the modern logic, especially as presented in the 
works of Lotze, Sigwart, Jevons, Green, Bosan- 
quet, and Venn. In the illustrations of the 
various inductive methods I have sought fresh 
material as far as possible, with the view of 
representing the actual modes of reasoning and 
methods of investigation employed by those who 
have become eminent in their several spheres of 
research, such as Faraday, Tyndall, Darwin, and 



PREFACE Xlii 

Lubbock ; and especially the different methods 
which have led to important discoveries in the 
various sciences. This applies not only to the 
illustrations in the text proper, but also to those 
which I have collected in Chapter XX. under the 
head of Logical Exercises. It seems to me, 
moreover, that inasmuch as the principles of 
inductive investigation are in such accord with 
the scientific spirit of our age, their importance 
as a logical discipline cannot be too highly valued. 

J. G. H. 

Princeton, N.J., March 2, 1896. 



INDUCTIVE LOGIC 

CHAPTER I 

The Nature of Inference 

Induction is a particular mode of inference in 
general ; and therefore before its nature and scope 
can be adequately defined, it will be necessary to 
give some account of the theory of inference, and 
its precise logical signification. Moreover, it is not 
possible to appreciate the distinction between the 
processes of induction and deduction, until we have 
first examined the characteristic features which 
are common to the two, and which constitute the 
essential elements of inference itself. The nature 
of inference may be unfolded in two ways. We 
may consider what it is in its outward aspect — 
that is, through its phenomenal manifestation in 
what it effects ; or it may be more strictly defined 
in terms of its warrant, or ground. From the first 
point of view we examine inference as regards its 
psychological significance; that is, what is infer- 
ence considered as a psychical experience, its na- 
ture and characteristics? But we must consider 
also the second question, whether there is any 

B 1 



2 INDUCTIVE LOGIC 

necessity limiting and determining the subjective 
experience, which presents the character of a law 
having universal validity. What goes on in the 
mind during the process of inference ? Also, what 
is the rationale of such a process ? These ques- 
tions we will examine more closely, in order to 
show the nature of inference under the two aspects, 
the one psychological, and the other logical. 

It is a well-recognized fact, in psychology, that 
in our simplest as well as the more complex per- 
ceptions, the interpretation of the data of presenta- 
tion always goes beyond the strict content of the 
data themselves. We see more than is given in 
the field of vision immediately before us. The 
mind supplies here and there the necessary parts 
that are lacking in the actual elements of presenta- 
tion, and yet which are necessitated by the known 
nature of that which is actually given. We form 
our judgment of distance indirectly, and not through 
direct presentation. So, also, our idea of a third 
dimension is acquired by a process, marvellously 
complex, in which the data both indicate and yet 
are transcended by the results. Whether the nativ- 
ist or empiricist holds the true position concern- 
ing original psychical experience, it still must be 
conceded according to either theory that the devel- 
opment of our perceptions corresponds to a law of 
growth based upon accumulated inferences. Infer- 
ence has been defined as the indirect reference of 
a content to reality, and as such, we see the be- 
ginnings of inference in the most simple of our 
perceptions. Every perception contains a direct 



THE NATURE OF INFERENCE 3 

reference to reality, but also something which in 
a greater or less degree is referred indirectly to 
reality. The fact that our knowledge as given in 
the complete perception contains more than is actu- 
ally mediated through the avenues of the senses, 
is due to the apperceptive processes of conscious- 
ness. Mind is active in perception, and not a mere 
passive receptacle. That which is given, the raw 
material of the senses, is elaborated and extended, 
as it is combined with the wealth of representative 
and conceptual material which the mind brings to 
every new perception. To this extent, at least, the 
mind possesses a creative function. A certain 
appearance of sky, combined with peculiar condi- 
tions of mind and temperature, leads one to assert, 
with some degree of certitude, that it will rain 
before morning. The prediction is an inference 
based upon, and growing out of, the actual data 
of perception, and yet far outrunning them. We 
recognize a friend from his step or voice. The 
mere presentation is only a sound. That it is 
associated with a person, and not an animal, or a 
thing, is an inference ; that this is the particular 
person whom we recognize as a friend and can call 
by name, even before we turn around to confirm 
the opinion by direct testimony of vision, this is 
a still further inference. And even when we open 
our eyes in simple vision itself, we fill up many 
a gap in our minds, and give depth and distance, 
and interpret the contrasts of light and shade, and 
the play of colors, through the process of inference, 
although we may not be aware of the process itself, 



4 INDUCTIVE LOGIC 

which is automatically operative through long-con- 
tiuued habit. When we thus regard inference as 
a psychological phenomenon, it may be readily ex- 
plained by the laws of comparison, association, 
recognition, generalization, etc. And, as such, in- 
ference has a subjective force at least, and leads to 
the habit of prediction and expectation. The will, 
influenced by the resulting belief, leads to activi- 
ties consistent with such expectation. 

Here, however, the question arises, which is 
urged with such force by Hume, Is there objective 
validity as well as subjective necessity ? This 
leads to a consideration of inference, from the sec- 
ond point of view, above mentioned. We may be 
constrained to believe certain things concerning the 
great world lying beyond the sphere of immediate 
consciousness ; but what warrant have we in so 
doing, or what assurance that our conclusions are 
correct ? May we not be deceived, after all, and by 
some psychological trick be led to regard the phe- 
nomena of consciousness as quite otherwise than 
that which obtains in reality? We may have a 
strong aversion to sitting down at a table where 
the number of persons will be thirteen. But has 
the subjective conviction, that one of the thirteen 
will die in the course of the year, any value when 
we come to refer it to reality, and ask ourselves the 
nature of the ground upon which the conviction is 
based ? 

On the other hand, however, it is quite a differ- 
ent kind of necessity which constrains us to judge 
that if a person jumps off of the roof of a house, 



THE NATURE OF INFERENCE 5 

he must surely fall to the ground below. Some 
grossly superstitious and ignorant people may be- 
lieve the former with as obstinate a conviction as 
the latter, so that a purely psychological criterion 
of the strength of conviction is not at all adequate 
or satisfactory. Is there any other criterion ? In 
what instances does this subjective constraint pro- 
ceed from the necessities of reality ? or, in other 
words, in what cases are Ave able to discover a logi- 
cally grounded warrant which compels the infer- 
ence, in distinction from the mere psychological 
compulsion which is occasioned by the psychical 
tendencies of association and generalization ? 

This leads us to consider the logical, in distinction 
from the psychological, nature of inference. Inas- 
much as the characteristic feature of inference con- 
sists in this, that while depending upon certain data 
of presentation, it nevertheless wholly transcends 
them, the question naturally suggests itself, whether 
it is something within the data themselves, or with- 
out, by virtue of which the mind thus goes beyond 
them in the process of inference. If it lies wholly 
without the data, it must be something imposed 
upon them by the mind, and as such can have only 
a psychological force and value. For instance, the 
belief that if thirteen sit down together at a table, 
one will die in the course of the year, can have only 
a subjective value and significance. This is true in 
all cases where the necessity of conviction finds its 
origin in prejudice or in superstition, or it may be 
in the force of authority. In all such instances we 
feel the lack of a satisfactory logical ground. How- 



6 INDUCTIVE LOGIC 

ever, on the other hand, if the data of consciousness 
contain within themselves that which enables us to 
transcend them at the same time that we interpret 
them, there is external validity for our inference 
that has a logical worth. This seems at the first 
glance to be a paradox. How can any content 
enable us to state concerning it more than is con- 
tained within it ? The answer to the seeming para- 
dox is that every concept, and every perception as 
well, have both an explicit and implicit content. We 
never attain complete vision or perfect apprehension. 
There are, moreover, many points of view, each 
giving additional knowledge concerning any phe- 
nomenon present in consciousness. We see, there- 
fore, only in part, and yet that which is seen contains 
certain necessary implications concerning that which 
is not seen. In the progress of knowledge, subse- 
quent observations, different points of view, are ever 
confirming and amplifying our inferences, enabling 
us to perceive immediately what formerly was only 
inferred. The process by which the implicit is 
becoming explicit indicates a necessary relation 
existing between that which is known mediately 
and that which is known immediately. Moreover, 
consciousness has been represented as a stream, or an 
intricately interwoven web, — something extremely 
complex. Every part is related both proximately 
and remotely. There is no such thing as an isolated 
perception ; every perception has its complex rela- 
tions and connections. So also every concept which 
is formed by generalization through comparison and 
abstraction, of our presentations as interpreted by 



THE NATURE OF INFERENCE 7 

us, possesses this characteristic of greater or less 
complexity. In this manner the world of conscious- 
ness is constructed ; that is, the world as it is for us. 
This forms a complex whole made up of parts, which 
in themselves may be regarded as wholes, and yet 
which may be still further divided and subdivided. 
Such an interrelated whole we may style a sys- 
tem, or, in other words, a complex whole whose parts 
are congruently arranged. The idea of system finds 
expression in the "Law of Totality," — that our 
knowledge is capable of arrangement in a self-con- 
sistent and harmonious system, and which moreover 
in its content and form faithfully represents objec- 
tive reality. 1 We find, therefore, that in the focus 
of consciousness at any one time, whether in the 
sphere of presentation or in the region of representa- 
tive or the conceptual processes, whatever is given 
carries with it always certain implications, and there- 
fore certain necessary relations. This is specially 
emphasized in Bosanquet's definition of system : 
"System is a group of relations, or properties, or 
things, so held together by a common nature that 
you can judge from some of them what the others 
must be." 2 Two facts regarded as independent and 
considered separately may give no information be- 
yond their explicit contents ; but when conjoined, 
they imply more than the sum of their parts. How 
often two ideas in separate minds yield no result; 
but brought together, they give light. Isolation 

1 Ueberweg, A System of Logic and History of Logical Doc- 
trine, pp. 540 f. 

2 Bosauquet, The Essentials of Logic, p. 140. 



8 INDUCTIVE LOGIC 

negatives inference. To unfold any data in all 
their manifold implications is the process of infer- 
ence. Its warrant lies in the fundamental postulate 
of knowledge which we are constrained to assume; 
namely, that our consciousness must be self-con- 
sistent throughout. Whatever is admitted as true 
must find a congruent place in the system to which 
it is possible to refer it. The necessity of fitting it 
in its proper place gives rise to certain implications 
which necessitate corresponding relations and attri- 
butes. And if it could not be put into such a place, 
we would feel that we should have to surrender the 
idea of self-consistency in the variously related ele- 
ments of our consciousness. The very integrity of 
our mental life necessitates this conviction. 

Therefore a part being given, we supply in our 
minds other parts, or the whole to which the given 
part must necessarily belong. To achieve this, with 
logical warrant, our knowledge of the part must be 
adequate to the extent that we know that the ele- 
ment under consideration cannot be complete in 
itself, but must be supplemented by its appropri- 
ately related elements which with it go to make up 
the complete system. We infer the nature of the 
flower not yet in bud, by the sprouting leaf. The 
one necessitates the other by virtue of their com- 
mon inherence in the same plant system. We 
know that figs do not come from thorns, nor grapes 
from thistles. Columbus, noting the seaweed, and 
birds, and the drift of the sea, inferred a shore 
beyond, to which he was constrained by the neces- 
sities of thought to refer them. It is said of Cuvier 



THE NATURE OF INFERENCE 9 

that he was able to reconstruct part for part the 
entire frame and organism of an animal whose 
fossil tooth alone formed the original datum. He 
knew the system to which it must have belonged 
and to which it alone could possibly be referred. 
An interesting quotation from Cuvier himself illus- 
trates most appropriately this function of inference. 
He says in his Ossemens Fossiles, " I doubt if any 
one would have divined, if untaught by observation, 
that all ruminants have the foot cleft, and that they 
alone have it. I doubt if any one would have 
divined that there are frontal horns only in this 
class ; that those among them which have sharp 
canines for the most part lack horns. However, 
since these relations are constant, they must have 
some sufficient cause ; but since Ave are ignorant of 
it we must make good the defect of the theory by 
means of observation : it enables us to establish 
empirical laws which become almost as certain 
as rational laws when they rest on sufficiently 
repeated observations ; so that now whoso sees 
merely the print of a cleft foot may conclude that 
the animal which left this impression ruminated, 
and this conclusion is as certain as any other in 
physics or morals. This footprint alone, then, 
yields to him who observes it the form of the 
teeth, the form of the jaws, the form of the verte- 
brae, the form of all the bones of the legs, of the 
thighs, of the shoulders, and of the pelvis of the 
animal which has passed by." 1 

In the common conduct of every-day life Ave infer 
1 Quoted by Jevous, Principles of Science, 2d ed. p. C83. 



10 INDUCTIVE LOGIC 

beyond the immediate present experience to future 
happenings and in a similar manner. My train is 
half an hour late. I know I must miss my connec- 
tions at the station ahead ; for the train I am hop- 
ing to catch at that place is scheduled to leave five 
minutes after the time of arrival of the train I am 
now on. The time relations here necessitate my 
missing my connections. This is rendered still 
more certain if they are rival roads ; on no account 
will one wait for the other. Moreover, the train I 
hope to make is made up and leaves the station in 
question, and so I cannot fall back upon the favoring 
chance that it also may be detained en route, and 
so enable me, after all, to reach it in time. Thus, 
with every additional knowledge of the system which 
forms the ground of my inference, and the various 
conditions which affect it, the validity of my infer- 
ence is thereby increased. Inference regarded as 
the analysis of a system of interrelated parts is 
illustrated in the following paragraph of Professor 
James : " The results of reasoning may be hit upon 
by accident. Cats have been known to open doors 
by pulling latches, etc. But no cat, if the latch got 
out of order, could open the door again, unless some 
new accident at random fumbling taught her to asso- 
ciate some new total movement with the total phe- 
nomenon of the closed door. A reasoning man, 
however, would open the door by first analyzing the 
hindrance. He would ascertain what particular 
feature of the door was wrong. The lever, e.g., 
does not raise the latch sufficiently from its slot — 
case of insufficient elevation — raise door bodily on 



THE NATURE OF INFERENCE 11 

hinges ! Or door sticks at top by friction against 
lintel — press it bodily down! I have a student's 
lamp of which the name vibrates most unpleasantly 
unless the collar which bears the chimney be raised 
about a sixteenth of an inch. I learned the remedy 
after much torment, by accident, and now always 
keep the collar up with a small wedge. But my 
procedure is a mere association of two totals, dis- 
eased object and remedy. One learned in pneumat- 
ics could have named the cause of the disease and 
thence inferred the remedy immediately/' 1 

Inference, therefore, may be regarded as a deep 
penetrating insight. The explicit is that which 
lies upon the surface, which the mind immediately 
grasps, for it lies directly in the focus of conscious- 
ness. Whereas the implicit is beneath the surface, 
and is revealed only through a searching analysis. 
This difference may be exhibited through the dis- 
tinction between the actual and the potential. A 
child regards gunpowder merely as a pile of coarse- 
grained sand. The man sees what the child sees, 
but also the existing possibilities under certain con- 
ditions of explosive force. He apprehends the 
potential as well as the actual ; and his inference 
as to the possible results is based upon his superior 
insight. It is therefore the well-furnished mind 
which sees things as most widely related, and dis- 
cerns the potential as well as the actual manifesta- 
tion, which will prove the most fertile in accurate 
inference, in prophetic suggestion, and in inventive 
resource. 

1 James, Psychologij, Vol. II. pp. 330, 340. 



12 INDUCTIVE LOGIC 

The whole world of reality, as well as that of 
knowledge, may be considered as one system, em- 
bracing within the unity of its totality all the vari- 
ous systems with their complicated parts. From 
this point of view everything bears relations to 
everything else in the universe. The original sig- 
nification of the term universe is thus emphasized. 
This thought, no doubt, Tennyson had in mind in 
the following verse : — 

Flower in the crannied wall, 

I pluck you out of the crannies, 

I hold you here, root and all, in my hand, 

Little flower — but if I could understand 

What you are, root and all, and all in all, 

I should know what God and man is. 

We can, in this connection, best exhibit the pre- 
cise nature and function of the universal in infer- 
ence. The possibility of unfolding the properties 
or relations of anything in all its implications 
depends upon our knowledge of the universal con- 
cept to which the properties or relations in ques- 
tion are naturally referred. While a singular 
proposition is the statement of the mere occur- 
rence of a phenomenon, the universal always 
implies a knowledge of the conditions and rela- 
tions of the phenomenon. 1 Insight is only pos- 
sible where there is a wealth of universal concepts. 
We see an animal which we observe to be cloven- 
footed. We infer that it also chews its cud. We 
do not observe this. The assertion does not arise 

i See Green, Philosophical Works, Vol. II. pp. 284, 285. 



THE NATURE OF INFERENCE 13 

directly from observed reality, but indirectly 
through the generic concept that has grasped to- 
gether the two attributes of chewing the cud and 
cloven feet as always and necessarily coexisting 
in one and the same animal Inference, in this 
sense, may be regarded as the indirect reference 
of knowledge to reality, and this is always medi- 
ated through the universal. The universal has 
this characteristic feature, that it preserves an 
identity in the midst of manifold differences. The 
same thought may be expressed by saying that the 
universal manifests a unity in the midst of diver- 
sity. However widely different, in many respects, 
the animals may appear that chew the cud, — as 
the cow, deer, sheep, etc., — there is always the 
constant characteristic that they are cloven-footed. 
Such a point of identity furnishes the constant 
factor which determines the nature and the validity 
of the inference. Were it not for this conceptual 
power of the mind, this ability to grasp phenom- 
ena in their universal essence, and consider them 
as interrelated and connected, we could never pass 
beyond individual and particular experiences which 
would form a series of wholly disconnected events. 
Knowledge could not then form a self-consistent 
system, or inference possess any higher worth than 
a haphazard guess. As Green says, " A ' mere 
fact,' a fact apart from relations which are not sen- 
sible, would be no fact, would have no nature, would 
not admit of anything being known or said about 
it." 1 

1 Green, Philosophical Works, Vol. IL p. 301. 



14 INDUCTIVE LOGIC 

Moreover, inference is not merely employed to 
extend the field of consciousness in unfolding sup- 
plementary elements lying beyond the sphere of 
direct cognition; the elements may all be given 
immediately, and inference employed to discover 
their connection and interrelations, by virtue of 
what bond they belong in one or the same sys- 
tem. Inference here functions as explanation. A 
man is found dead ; there are many wounds upon 
his person, evidences of a struggle in an out-of-the- 
way place upon a lonely road. Such a combina- 
tion of facts calls for an explanation which shall be 
consistent with them. The facts must all be cor- 
related in a system whose related facts and the 
unity of the whole will completely satisfy the 
mind. The mind is satisfied only when all hang 
together in what seems the only possible self- 
consistent co-ordinated system. The facts being 
given, they must be read backward to their origin. 
The other aspect of inference is the reading of 
facts forwards, or unfolding them in their neces- 
sary consequences. Inference is the reply to the 
natural questions of the mind, — whence and 
whither ? And the process is essentially the same, 
whether its peculiar mode consists in the evolu- 
tion or the involution of that which is given in 
consciousness. 

Moreover, the mere psychological inference, the 
subjective extension of the data of consciousness 
without any objective ground or warrant, should 
ever be corrected, or even at times wholly set aside 
by means of the truly logical inference. Where 



THE NATURE OF INFERENCE 15 

the psychological experience, in transcending simple 
presentation, proceeds upon strictly logical grounds, 
and has objective validity as well as subjective 
necessity, we possess a warrant of the highest pos- 
sible worth. 



CHAPTER II 

Induction and Deduction 

There have been divergent tendencies in the 
history of logic, to make either deduction or in- 
duction alone the whole of logical procedure in the 
process of inference. The fact that the Aristotelian 
logic, which is essentially deductive, has been for 
centuries exclusively associated with logic as a 
whole, has left the impression upon many minds 
that it is the beginning and end of the logical en- 
cyclopaedia. On the other hand, J. S. Mill and his 
followers have attempted to analyze the syllogism 
to prove its essentially inductive character; and 
they have maintained that all reasoning is induc- 
tive. This is the position in the main of Bacon, 
Locke, and Bain. Locke, for instance, insists that 
the syllogism is of less value than external and 
internal experience, induction, and common sense. 1 

So also, in a similar vein, Schleiermacher says: 
"The syllogistic procedure is of no value for the 
real construction of judgments, for the substituted 
judgments can only be higher and lower ; nothing 
is expressed in the conclusion but the relation of 
two terms to each other, which have a common 

i Essay on Human Understanding, Book IV. p. 7. 
16 



INDUCTION AND DEDUCTION 17 

member, and are not without, but within, each 
other. Advance in thinking, a new cognition, can- 
not originate by the syllogism ; it is merely the re- 
flection upon the way in which we have attained, or 
could attain, to a judgment, the conclusion ; no 
new insight is ever reached." * The two opposed 
views thus indicated do not necessitate conflicting 
or mutually exclusive processes. It is better to 
regard them, not as radically different types of 
inference, but rather as different phases of one and 
the same inferential process. We have seen that 
inference consists in interpreting the implications 
of the system to which the given in consciousness 
belongs. In the light of this definition we can best 
indicate the relative functions of induction and de- 
duction in the process of inference. When the 
system can be considered as a whole, and is appre- 
hended in its entirety, then it may become the 
ground upon which the inference is based, resulting 
in unfolding the necessary nature or relations of 
any of the parts considered in themselves, or in 
reference to the system as a whole. The procedure 
in such a case is from the nature of the whole 
system, to the nature of the several parts, and their 
existent relations, and this is deductive in its es- 
sential features. 

On the other hand, when we know the various 
parts, and proceed from them as data to construct 
the system which their known nature and rela- 
tions necessitate, it is induction, or procedure from 
elementary parts to the whole thus necessitated. 

1 See Ueberweg, System of Logic, etc., p. 345. 
c 



18 INDUCTIVE LOGIC 

From a knowledge of the planetary system, we 
can infer the necessary positions of sun, moon, and 
earth at any required time, as, for instance, in the 
calculation of an eclipse. This is deduction. But 
when we begin with investigating the several move- 
ments of the different planets, and from them infer 
the necessary nature of the system of which they 
are parts, we have the process of induction. Such 
processes we see must be complementary, and mu- 
tually dependent. As Lavater says, " He only sees 
well who sees the whole in the parts, and the parts 
in the whole." 

Moreover, the distinction between deduction and 
induction may be shown through their respective 
relations to the universal, which we have seen is the 
ground of inference. The question whose answer 
leads to the deductive process in reasoning, is, What 
does the universal necessitate ? In induction, the 
question which starts the investigation is, Into 
what system may I construct the given material 
properties or relations, so as to reach a universal 
concept that will be consistent with itself and with 
the whole of knowledge which forms the world of 
consciousness? In this there is an analytical dis- 
crimination of the essential and accidental elements, 
and the gathering- together of the former into the 
complex whole which is the universal. Induction, 
therefore, is inference viewed from the side of the 
differences ; deduction is inference viewed from that 
of the universal. For instance, we may investigate 
the characteristic features of a diamond, and find 
that a certain specific gravity, 3.53 as compared with 



INDUCTION AND DEDUCTION 19 

water, is a constant and determining attribute, and 
as such must be incorporated as an essential element 
of the general concept diamond. We can then form 
the universal judgment. Whatever stones possess 
this specific gravity are diamonds. Their differences, 
regarding size, brilliancy, etc., may all be set aside 
as accidental, but the one constant determining 
feature indicates a oneness in which they all agree. 

And so with the other essential attributes. After 
possessing such knowledge gained inductively, we 
may use it practically in a deductive manner; 
and it is so used in discriminating between true 
and imitation stones, as described in the following 
process : " Diamonds, rubies, and sapphires are 
now tested by floating to prove their genuineness. 
The liquid used has five times the density of water, 
and is composed of double nitrate of silver and 
thallium. The tests are rapidly made, as all stones 
of the same nature have the same specific gravity, 
while none of the bogus ones have the same weight 
as those they are made to imitate." 

Another view of the relation of induction to de- 
duction may be gained by calling attention to the 
difference of significance between the terms, a truth 
and a fact. A fact carries with it only the special 
and individual character of the particular occur- 
rence in which it is manifested. A truth, however, 
is always universal in its very nature, admitting of 
universal application, and capable of illustration 
in an indefinite number of different facts which 
embody its essence. In deduction we have given 
some truth of universal nature that leads to indi- 



20 INDUCTIVE LOGIC 

vidual facts that may be subsumed under it. In 
induction, we interpret a -fact or a number of facts 
in the light of their universal implication, on 
the ground that there can be no such thing as 
an isolated fact, but every fact must have some 
relation to a universal to which it must be referred. 
While considering the distinctions between in- 
duction and deduction, we must not overlook their 
mutual dependence. We cannot proceed in de- 
duction irrespective of induction, because the uni- 
versal upon which the deductive process is based 
arises in the majority of cases from a previous 
induction. It is true that the universal term may 
be in a proposition that is known a priori, as the 
axioms of geometry and certain space and time 
postulates ; but a very small proportion of major 
premises can be said to have such an origin, and 
their resulting conclusions have very slight ma- 
terial significance. Deduction that reaches other 
than purely abstract and formal conclusions must 
rest upon induction for the material to form its 
premises. We find this even in the technical con- 
struction of the syllogism, where, for instance, the 
question of the distribution of the terms is raised. 
We may insist that a certain middle term is dis- 
tributed as it is the subject of an universal affirma- 
tive proposition ; but then the further question 
naturally suggests itself, How do we know that 
the proposition in question is really a universal ? 
Its material significance alone tells us that we 
may write it as an A or / proposition, as the case 
may be. The matter is a function of the form, 



INDUCTION AND DEDUCTION 21 

and the form a function of the matter. They can- 
not be separated in fact, unless we conceive reason- 
ing as a purely formal process of determining a 
conclusion, irrespective of the truth or falsity of 
the premises. If we regard the premises as 
given, and we accept them with unquestioning 
credence, the deduction is purely formal ; so 
also if the various terms are expressed by letters 
A, B, C, etc., and devoid of any material signifi- 
cance. Any process of reasoning based upon a 
slavish acceptance of premises can only reach 
artificial and even false results. In the actual ex- 
periences of life our premises are not made for 
us. They must be constructed by us through our 
interpretation of reality. Disregard of this has 
brought formal logic into much disrepute, and it 
has often degenerated into the barren discussion of 
logical puzzles and quibbles. Grant a person any 
premises he may choose to assume, irrespective of 
an inductive test of their validity, he can prove 
black white, and white black. 

On the other hand, induction is dependent upon 
deduction ; for we cannot reason from particular 
instances to a universal proposition, unless we as- 
sume as basis of the whole inductive process some 
postulate which has real universal significance. 
Otherwise, we reach only a high degree of prob- 
ability, but not necessity; a rude generalization, 
but not universality. When we assert some such 
general statement as this, that arsenic always acts 
as a poison, we have the universal character of the 
proposition upon an underlying postulate that is 



22 INDUCTIVE LOGIC 

understood even though it is not expressed, such as 
the uniformity of nature ? that under identical con- 
ditions we always look for identical effects. This 
will be discussed later more in detail ; it is re- 
ferred to at this point merely to illustrate the de- 
ductive basis of induction. Bradley insists that 
there can be no such thing as induction, because it 
always rests upon an implied universal which gives 
to the process as a whole a deductive character. 1 
His criticism has the force only of proving that 
induction cannot be independent of deduction. 
This dependence does not, however, necessarily 
vitiate the integrity of induction as a mode of the 
inferential process. ( Lotze has placed special em- 
phasis upon this dependence of induction upon 
deduction. He says : " It is the custom in our 
day to collect into one body the numerous opera- 
tions which assist us in ascending from particulars 
to generals, or to call this inductive logic, and to 
set it against the deductive or demonstrative logic 
along with much disparagement of the latter. Such 
disparagement rests on a mistake. The inductive 
methods, it is certain, are the most effectual helps 
to the attainment of new truth, but it is no less 
certain that they rest entirely on the results of 
deductive logic." 2 

Moreover, in induction the results obtained and 
formulated in general propositions may be extended, 
and often modified by a deduction which is based 

1 Bradley, Principles of Logic, p. 332. 

2 Lotze, Logic, p. 288. See also Bosanquet, Logic, Vol. II. 
p. 119. 



INDUCTION AND DEDUCTION 23 

upon them as major premises ; for the deduction 
thus proceeding from them reveals new instances 
which conform or perhaps modify the simple induc- 
tive results themselves. What is popularly called 
a hasty generalization, if made a major premise of 
a syllogism, will often lead us astray through the 
deductions drawn from it. As soon as we are aware 
of this, we return to question the validity of the 
generalization, whose weakness is not appreciated 
until thus tested and revealed. Thus deduction 
serves to extend and correct the results of induc- 
tion, and at the same time it itself is dependent 
upon the results of inductive generalization for the 
material to form its premises. We come to see, 
therefore, how intimately associated these two proc- 
esses are in actual reasoning. For convenience of 
illustrating their individual characteristics, they 
may be considered as separate, and each investigated 
as an independent mode of inference. But they are 
in reality mutually related and dependent, and are 
always found manifesting their functions together. 
In any course of reasoning concerning the conduct 
of our every -day affairs, or in scientific investigation, 
anywhere, indeed, outside of the artificial examples 
of logical text-books, we reason both inductively and 
deductively in one complex process. 



CHAPTER III 

The Essentials op Induction 

We now proceed to a more precise determination 
of the nature of induction. Its point of view in all 
reasoning regards concrete instances. They are the 
data, and from them general propositions are to 
result. The procedure is from given facts to laws 
which are the ground and explanation of these 
facts. We are here, however, at once struck with the 
evident break in the course of our reasoning. Pro- 
cedure from the particular to the universal cannot 
be a continuous process. There is a gap somewhere. 
The conclusion contains more than the premises. 
In deduction, we are proceeding from the greater 
to the less, and we experience no violation of our 
logical sense ; but at once we appreciate the diffi- 
culty which attends the reverse process, from the 
less to the greater. Here we soon reach a point 
where we pass beyond the sphere of our experience 
to the generalization which necessarily embraces 
far more than our experience. This is the so-called 
inductive leap ; or it is sometimes referred to as the 
inductive hazard. But is this a leap in the dark 
— a wild guess concerning all that lies beyond the 
sensuous sphere ©f our immediate experience ? This 
24 



THE ESSENTIALS OF INDUCTION 25 

would be the ease, were we compelled to use the 
mere data of experience as sole ground for our 
inferences. John Stuart Mill insists that nothing 
whatever is given in consciousness but particular 
sensations, and these are but subjective states of 
feeling, and with no assurance of any definite cor- 
respondence with the external world. With such 
purely empirical data it is impossible to proceed to 
truths of universal validity. It is necessary to post- 
ulate some universal truth which the mind through 
strictly a priori considerations is constrained to 
formulate, and which will serve to bridge the gulf 
between the particular and the universal. 

This postulate— lias been variously expressed by 
different authors, yet with substantially the same 
significance in all. In the older logic, it is put 
under the convenient formula of the uniformity of 
nature ; that is, that beyond the sphere of experi- 
ence, phenomena will behave in the same manner, 
under like conditions, as in the sphere of immediate 
observation and experiment. In the modern logic 
this is somewhat differently expressed. The phrase 
" uniformity of nature," being somewhat indefinite 
and implying a point of view purely objective, is 
not used. Modern writers have omitted it largely 
from their terminology. Lotze says : "The logical 
idea upon which induction rests is by no means 
merely probable, but certain and irrefragable. It 
consists in the conviction, based upon the principle 
of identity, that every determinate phenomenon M 
can dei jend upon only one determinate condition, 
and accordingly that, where under' apparently dif- 



26 INDUCTIVE LOGIC 

ferent circumstances or in different subjects P, S, 
T, U, the same M occurs, there must inevitably be 
in them some common element 5 which is the true 
identical condition of M, or the true subject of MP x 
We have a somewhat similar description of the 
basis of the inductive process given by Sigwart: 
"The logical justification of the inductive process 
rests upon the fact that it is an inevitable postulate 
of our effort after knowledge that the given is 
necessary, and can be known as proceeding from its 
grounds according to universal laws." 2 Bosanquet 
considers as the basis of inductive inference that 
which he calls the postulate of knowledge, that " the 
universe is a rational system, taking rational to mean 
not only of such a nature that it can be known by 
intelligence, but further of such a nature that it 
can be known and handled by our intelligence." 3 

I have quoted these passages from Lotze, Bosan- 
quet, and Sigwart, that we may appreciate the mod- 
ern tendency to derive the inductive postulate from 
an epistemological source ; namely, that our knowl- 
edge must be consistent throughout with itself, 
part to part, and parts to whole, and that the world 
for us is the world as constructed by our knowledge. 
Whatever is given in consciousness must belong 
therefore in the one place where it appropriately 
and necessarily belongs. Here also there must be 
a place for everything, and everything in its place. 
There must be a uniformity of consciousness ; that 

1 Lotze, Logic, p. 102. 

2 Sigwart, Logic (Eng. translation), Vol. II. p. 289. 

3 Bosanquet, The Essentials of Logic, p. 166. 



THE ESSENTIALS OF INDUCTION 27 

is, the primary postulate and the uniformity of 
nature is secondary to this, and implied in it. This 
postulate may also be expressed as follows : What 
is once true, is always true. Here true is used in 
the sense of the universal significance of a fact. 
Whenever a concrete instance is present in con- 
sciousness, its existence must be considered as 
necessitated by some antecedent which can satis- 
factorily account for it, and which can at the same 
time be appropriately adjusted to the whole of our 
knowledge in interpreting it. Bosanquet says that 
"ideally speaking every concrete real totality can 
be analyzed into a complex of necessary relations." l 
These necessary relations of course have a universal 
significance, and therefore in every concrete in- 
stance, if we can rightly interpret it, we may dis- 
cern the universal element which is contained in it, 
and gives it a place and meaning in the world as 
cognized by us. 

There is a sense in which induction may be re- 
garded as the inverse process of deduction. In 
deduction the problem is concerned with the ques- 
tion, What does the universal necessitate ? In 
induction, the instance is given, and the problem 
is, What universal can be discovered which could 
give rise to the instance in question ? This view 
of induction is especially associated with the name 
of Jevons, whose inductive system is described as 
the inverse of deduction. He calls it the decipher- 
ing of the hidden meaning of natural phenomena. 2 

1 Bosanquet, Logic, Vol. II. p. 82. 

2 Jevous, Principles of Science, p. 124. 



28 INDUCTIVE LOGIC 

The name commonly used to designate this view of 
induction is that of "reduction," originally sug- 
gested by Duhamel. 1 This process was known to 
the old logicians, who called it " Method " to denote 
the process of hunting for middle terms by the aid 
of which a given conclusion could be proved. 2 Like 
all inverse processes, it is by itself an indeterminate 

one. 

Given All A is B, and 

All B is C, 

we infer by the direct process of deduction that 

All A is C. 

But in the indirect or inverse process we have 
given all A is G, and the problem, to find a middle 
term which necessitates such a conclusion, is an 
indeterminate one. There may be a number of 
middle terms. This is analogous to the method 
of integral calculus ; while differentiation leads to 
a definite result, the inverse process of integration 
leads to an indeterminate result. So also we mul- 
tiply two numbers, producing one determinate re- 
sult ; but inversely, when we have given a certain 
number, and ask what factors multiplied together 
could produce this number, we may reach several 
different solutions. The answer is indeterminate. 
Professor Jevons, in his scheme of inductive infer- 
ence, falls back upon probability to indicate which 
of several possibilities is the most likely one in the 

1 Duhamel, Methodes, Vol. I. p. 24. 

2 Venn, Empirical Logic, p. 361. 



THE ESSENTIALS OF INDUCTION 29 

given case. 1 But before the inverse operation can re- 
sult in determinate results, the given terms such as 
A and (7 must be subjected to some analysis in order 
that their material signification may give sugges- 
tion as to the nature of the middle term. For in- 
stance, a man is found dead, washed ashore by the 
tide ; the natural supposition would be that he met 
his death by drowning. And yet it might possibly 
happen that the man died through injuries inflicted 
by blows, or by poison, or heart failure. The at- 
tendant circumstances and bodily indications must 
suggest the most probable cause to account for the 
given effect. Venn criticises Jevons' view of induc- 
tion, making it the inverse process of deduction, on 
the ground that it is purely a formal process, and 
therefore can lead only to indeterminate results. 2 

It is always possible, however, to make some 
analysis of the material significance of the data, as 
has been above indicated, which relieves the purely 
formal processes from the indefiniteness of the re- 
sults. Bosanquet criticises Jevons' theory of in- 
ductive inference, in that the hypothesis proposed 
to account for the given in reality can at best be 
only highly probable. 3 However, Venn, Lotze, Bo- 
sancpiet, Sigwart, all allow a place to the inverse 
function of all inductive reasoning; their conten- 
tion, however, is this, that it does not furnish an 
adequate account of the whole matter. 4 

1 Jevons, Principles of Science, p. 219. 

2 Empirical Logic, p. 359. 

3 Bosanquet, Logic, Vol. II. p. 175. 

4 Venn, 361; Bosanquet, Vol. II. p. 175; Sigwart, Vol. II. 
p. 203, 289. Lotze, Outlines of Logic, p. 93. 



30 INDUCTIVE LOGIC 

It is interesting to note that WhewelPs theory of 
induction corresponds in the main to this idea of 
reduction, or inverse process. He finds in induc- 
tion a twofold operation of the mind, consisting in 
the colligation of facts and the explication of con- 
ceptions. By the colligation of facts he refers to 
that insight which is able to see the connections 
and relations which necessarily exist between the 
different phenomena present in consciousness ; and 
by explication of conceptions he refers to the ap- 
propriate fitting in of these related facts to some 
conception of the mind which most readily ac- 
counts for them. 1 Such a process is merely the 
reading of given facts backward to their origin, 
or substantially an inverse process, where the pro- 
cedure is from the given concrete to the explanation 
of the same in terms of the universal to which it 
can be most appropriately referred. So also Mill's 
account of procedure by hypothesis, as we shall see 
later on, presents characteristics similar to this 
process of reduction. 

The end of induction is to discover a law having 
objective validity and universal application. There 
is a distinction which must be noticed and clearly 
kept in mind ; namely, the distinction between a law 
and a rule. Induction seeks a law, and not a rule. 
A law expresses the essential and universal rela- 
tions subsisting between given phenomena, elimi- 
nating entirely all accidental and local coloring. A 
law has objective validity, and preserves a constant 
nature. There can be only one law in reference 

1 Whewell, Philosophy of the Inductive Sciences, pp. 172, 202. 



THE ESSENTIALS OF INDUCTION 31 

to one and the same connection of facts. A rule, 
however, is subjective, dealing with the individual's 
attitude to phenomena, rather than an explanation 
of the essential features of the phenomena them- 
selves. It often is determined in the concrete by 
that which is external, local, and accidental. There 
may be many rules, varying with many minds and 
many climes. Fundamental and universal laws of 
political economy become maxims and rules in dif- 
ferent communities. The laws of morality, univer- 
sal and immutable, become rules of conduct in in- 
dividual experience admitting of wide difference of 
opinion and diversity of application. 1 In the proc- 
esses of induction, therefore, the law is the desidera- 
tum, and not the rule. 

Law, however, is used rather loosely in our ordi- 
nary terminology. Law as used in jurisprudence 
has a meaning quite different from law as used in 
physical science. And so, also, the laws of biology, 
the laws of political economy, the laws of ethics, 
are referred to with different shades of meaning in 
each sphere. However ambiguous may be the sig- 
nificance of " law " in ordinary thought and usage, 
nevertheless in induction it has a constant and a 
simple significance, which if carefully adhered to 
will avoid confusion, and obscurity as well, in our 
inferential processes and results. Law in induction 
is always in the form of an hypothetical universal : — 

If A is, B is. 

It does not assert what has happened, but what 
1 Lotze, Logic, p. 335. 



32 INDUCTIVE LOGIC 

should happen under certain conditions. Given 
the antecedent A, a certain determinate consequent 
B is always necessitated. The relation is constant 
and invariable, and therefore has a universal signifi- 
cance. 

Induction holds a peculiar and important place 
in our every-day life, because it has to do with the 
analytical treatment of instances as they appear in 
experience. The large part of our conscious think- 
ing has to do with the concrete, the raw material 
of experience ; this, induction alone can handle. 
Leonardo da Vinci's maxim was " to begin with ex- 
perience and by means of it to direct the reason." 1 
Thus the superstructure of knowledge is raised day 
by day. The given is continually being interpreted 
and referred to its appropriate place, as the stones 
of the quarry are hewn and fitted in their proper 
position in the building for which they have been 
designed. There are certain individual experiences 
which it is impossible to determine through our 
syllogistic forms. They cannot be judged deduc- 
tively. There is no general category under which 
they can be subsumed. They may be formally 
illogical if thus expressed, and yet admit of direct 
investigation and experiment in an inductive man- 
ner, for the purpose of disclosing the law under- 
lying them and as yet unknown. 

It often happens that through indifference or 
indolence, we are content to refer many phenomena 
to long-established and convenient categories, which, 
if investigated independently, we would find could 

1 Ueberweg, Logic, p. 42. 



THE ESSENTIALS OF INDUCTION 33 

not possibly be so treated. The convenient pigeon 
hole, because near at hand, receives much that does 
not properly belong there. It is the office of induc- 
tion to investigate anew the old material, and then 
to reclassify in accordance with the revised gen- 
eralizations which such investigations may neces- 
sitate. 

The procedure by induction is in keeping with 
the scientific spirit of the day, — to interpret the 
phenomena of nature as given, and not to antici- 
pate nature through preconceptions, and wrest fact 
in order to fit theory. It comes to the sources in 
nature with empty vessels to draw and carry away 
that which nature alone can give. 



CHAPTER IV 

Types of Inductive Inference 

The process of induction, as we have seen, is a 
procedure from given instances to the discovery of 
the law which underlies them, and which is the 
ground of the connection of the various attributes 
and relations that unite in the one concrete whole. 
Viewed from the standpoint of the direction of the 
process, we have found that it is always towards 
some general expression of individual experiences, 
and in this respect it is the inverse of deduction, 
which proceeds from the general to the particular 
which is embraced in it. There is, however, another 
and important point of view that should not be over- 
looked. We have to consider the mode of the proc- 
ess as well as its direction ; not merely the result 
to be attained, but also the peculiar manner of 
realizing the same must be considered. Difference 
in method here gives rise to various kinds of induc- 
tive inference. The end proposed in all is to gen- 
eralize our experiences as they occur in the concrete 
and particular. When I find a given phenomenon, 
A, given in consciousness, and characterized by 
several distinctive features among which I note 
specially the mark B, the question at once most 
34 



TYPES OF INDUCTIVE INFERENCE 35 

naturally suggests itself Is there a reasonable 
expectation that I shall always hud B as an insep- 
arable accompaniment of A, so that I can assert 
confidently that whenever A is found, B also will 
be found ? There are three ways of satisfying 
ourselves as to the existence of any constant rather 
than coincidental connection between antecedent 
and consequent, as A and B. These give rise to 
three different methods of inductive research, and 
they are as follows : — 

I. The Method of Enumeration. 
II. The Method of Comparison, or Analogy. 

III. The Method of Scientific Analysis, or 
Search after Causal Connection. 

Failure to distinguish between the three methods 
has given rise to confusion in the definition of and 
corresponding reference to inductive inference ; 
some authors use induction in one, and some in 
another of these senses. It is necessary to dis- 
criminate carefully, and to maintain a strict con- 
sistency in the usage of the terms as defined. 

I. The Method of En umeration. — We observe the 
various instances in which certain attributes, as A 
and B, are conjoined in our experience. We count 
them in the sense of noting to what extent they 
accumulate, without noticing any exception to what 
seems at least an invariable connection. We do 
not necessarily count by precise enumeration reach- 
ing a numerically definite result. We notice 
merely to what extent the observed instances of 
like nature accumulate ; that is, whether a few, a 
considerable number, or a very large number. The 



36 INDUCTIVE LOGIC 

mere number of instances produces a certain psycho- 
logical impression, whatever may be their logical 
force. This is brought about through the laws of 
association, and creates an expectation of a con- 
tinuous repetition of the experience in question. 
This arises from a natural tendency of the mind to 
generalize. We observe that crows are black ; and 
the increasing number of confirming instances goes 
far to establish a connection between the crow and 
its color which seems to have universal validity. 
The enumeration of instances may lead us to any 
one of three results : — 

1. We may meet with no exception whatsoever, 
until the scope of observation completely embraces 
the sum of all possible instances. This is complete 
enumeration, and when enumeration reaches this 
limit, it passes over into deductive reasoning, by 
virtue of the logical canon that whatever is true of 
the parts is true of the whole distributively ; that is, 
provided the summation of the parts has been an 
exhaustive one. We assert that all the sheep of a 
given flock are white ; for we have observed each 
separately and no one has been missed in the count. 
So, also, the judgment that all planets move around 
the sun, resulting from an enumeration of the planets 
one by one. It is possible also to have a perfect in- 
duction with an infinite enumeration of parts. This 
is possible in two cases, as pointed out by Beneke. 1 
First, when the parts are connected together contin- 
uously in space, so that a survey of all is possible 
in a finite, and often a very short time. This occurs 

1 Quoted by Ueberweg, Logic, p. 482, 



TYPES OF INDUCTIVE INFERENCE 37 

in geometrical demonstration when the inference, 
based upon the simple figure it refers to, is extended 
to all figures falling under the like definition. And 
second, when the parts are not continuously con- 
nected, if it can be proved syllogistically that what 
is true of a definite nth part, must also be true for 
the (n + l)th part. 

Perfect induction also embraces arithmetical 
method and computation. Here the whole, which 
is the sum of the facts in each case, is a totality 
or universal whose differences, which are all sepa- 
rate and distinguishable, are yet homogeneous and 
equal. 1 There is no qualitative differentiation of 
parts, only a quantitative one. The total is the 
sum of the units, and each unit is like every other 
one. If we have one hundred units making a 
totality, the one that may be the twenty-seventh 
is precisely like the sixty-seventh. It is a case 
where each one counts for one, and no one for 
more than one in an absolutely literal sense. 

It has been urged against perfect induction that 
it affords no new information, and, therefore, its 
results are not valuable. However, the summation 
of particulars in abbreviated forms is always an 
advantage. It is a labor-saving process to the mind. 
It enables the mind to. retain a large number of 
facts by throwing them into one and the same cate- 
gory; and it facilitates arithmetical processes by 
convenient comprehending of units within a totality. 

2. The second result that is possible, is that, in 
counting instances, our enumeration should prove 
1 Bosanquet, Logic, Vol. II. p. 54. 



38 INDUCTIVE LOGIC 

incomplete. From the necessities of the case, we 
are often not able to observe the entire sphere of 
possible occurrences and cover the whole ground. 
It may be that beyond the sphere of our expe- 
rience, the constant connection between certain 
phenomena may be disturbed by the appearance 
of some variable factor of which we have been 
wholly ignorant. It is the possibilities beyond 
the sphere of observation which render uncertain 
the results of our count. We are sure as far as we 
have observed ; but we have not gone far enough 
perhaps. Such results, formulated in general prop- 
ositions, are termed empirical laws ; that is, gen- 
eralizations from an experience necessarily limited. 
3. We have still a third case ; where in our 
enumeration of positive instances we meet with 
exceptions to a greater or less extent. Here we 
cannot even sum up the actual experience in terms 
of a generalization. There are outstanding excep- 
tions which will invalidate it. We must, therefore, 
fall back upon the theory of probability and the 
calculation of chances, presuming that, in general, 
we will meet with the same proportion of excep- 
tions to positive instances in the future, that we 
have already observed in the past. So we make, 
in our minds at least, comparative tables of posi- 
tive cases over against exceptions, and reach a 
summary of the result in the form of a ratio, 
whose numerator will be the number of positive 
cases observed, and the denominator the total num- 
ber of instances including positive instances and 
the corresponding exceptions. We observe that 



TYPES OF INDUCTIVE INFERENCE 39 

some cryptogamous plants possess a purely cel- 
lular structure ; others, however, do not, being 
partially vascular. The probability that a new 
cryptogam will be cellular can be estimated only 
on the ground of the comparative number of 
known cryptogams which are cellular, as over 
against the total number of cryptogams, both cel- 
lular and vascular, previously observed. 1 

II. The Method of Analogy. — Here, also, we 
start with the experience that A is characterized 
by the mark B. But there is additional knowledge 
of which we may avail ourselves in the generaliza- 
tion of some past experience already effected, such 
as the following : that A very closely resembles C, in 
that the two have many properties or attributes in 
common. The inference by analogy is that Calso, as 
well as A, will have the mark B. It may be that we 
cannot examine C in a number of various instances 
to see in how many the mark B occurs. Our only 
resource is the inference which is based upon the 
known resemblances, or analogies. This kind of 
inference, for example, was employed by Sir Isaac 
Newton in a very interesting manner. He had ob- 
served that certain "fat, sulphureous, unctions 
bodies," such as camphor, oils, spirit of turpentine, 
amber, etc., have refractive powers two or three 
times greater than might be anticipated from their 
densities. He noticed also the unusually high re- 
fractive index of diamond, and from this resem- 
blance, based upon similarity in reference to one 
attribute only, he inferred that diamond also would 

1 Jevous, Principles of Science, pp. 146, 147. 



40 INDUCTIVE LOGIC 

prove to be combustible. His prediction in this 
regard was verified by the Florentine Academicians 
in 1694. 1 Brewster made a striking comment upon 
Newton's inference, to the effect that if Newton 
had drawn a like analogy in reference to greenock- 
ite and octahedrite as he did concerning diamond, 
inasmuch as they, too, have a very high refractive 
index, he would have been wholly incorrect. This 
is an indication of the fact that argument by anal- 
ogy is not conclusive. 

Bosanquet has very strikingly expressed the es- 
sence of the analogical method in saying that "in 
Analogy we weigh the instances rather than count 
them." 2 The distinction between analogy and 
enumeration of instances lies in this, that in the 
former we count similar attributes in the contents 
of two instances, and balance them against the dis- 
similar or unknown. In induction by enumera- 
tion we count similar instances, considering them 
in their totality without examination and compari- 
son of their respective attributes. 

III. The Method of Scientific Analysis. — The 
instance in question, A, which is characterized by 
the mark B, is subjected to a vigorous analytical 
examination, to show that A and B are related 
through a causal connection. This analysis is 
effected either through a minute observation or 
by means of exact experiment. The end to be 
attained by such analysis is to separate a complex 
phenomenon into its several elements, by which 

1 Jevons, Principles of Science, p. 527. 

2 Bosanquet, The Essentials of Logic, p. 155. 



TYPES OF INDUCTIVE INFERENCE 41 

process a causal connection may be revealed, whose 
very existence is disguised by the complexity of 
the phenomenon. For instance, the phenomenon 
of death following the taking of arsenic is an 
event so complex as to evade a precise determina- 
tion of the causal relation. When analyzed into 
simpler elements, it is found that the immediate 
effect of arsenic upon the bodily tissues is to 
harden them so as to prevent their normal function- 
ing. This is the causal ground of the death due to 
arsenic. Moreover, this analytic process, which 
may be appropriately called a material one, is sup- 
plemented by a formal process of negation, that is, 
an instance in which the suspected causal element 
is absent in the complex phenomenon under in- 
vestigation, and the related effect, before observed, 
now no longer appears. This formal process acts 
as a check, and as a verification as well, of the 
material analysis of the phenomenon. For ex- 
ample, an antidote, as sesquioxide of iron, being 
administered, no death from arsenic occurs ; and it 
is also observed that no hardening of the tissues 
has resulted, therefore the former result, hardening 
of tissues producing death, has been thus corrobo- 
rated negatively by the fact that where no harden- 
ing of tissues has resulted, death does not follow. 

We see at once the advantage of such a method 
over that of counting all instances where taking of 
arsenic has caused death. The latter is a phenom- 
enally adjudged result ; the former penetrates with 
analytic insight to the ground of the phenome- 
non itself. Thus one instance, if its parts and their 



42 INDUCTIVE LOGIC 

manifold, relations are adequately comprehended, 
may suffice for a universal conclusion based upon it. 
It is true, however, as remarked by Bosanquet, that 
" number of observations does, as a rule, assist analy- 
sis and contribute to eliminating error. Scientific 
analysis as such, however, does not deal with in- 
stances, but only with contents." l 

In cases where the phenomenon does not reveal 
its component elements under observation, and it is 
impossible to subject it to experiment, the most 
likely cause of the effect in question is tentatively 
judged to be the real cause, until it can be verified 
in reality. This is procedure by hypothesis, and 
is always resorted to as preliminary to a subsequent 
experiment which is its test, or else in lieu of such 
an experiment when it is by the nature of the case 
precluded. It is a form of ideal analysis. The ex- 
periment is constructed mentally. The phenome- 
non is separated into what we would reasonably 
imagine its simpler elements would be. We are 
constrained to believe that if the hypothetical ante- 
cedent existed, it would be adequate to produce the 
effect. Although rising in the sphere of the imagi- 
nation, it is that with which the mind is, for the time 
at least, satisfied as an explanation of the facts which 
demand some cause to account for them. Regard- 
ing induction as a process of reduction, hypothe- 
sis is the assumed universal, or middle term, which 
will necessitate the phenomenon under investiga- 
tion as its logical conclusion. 

We will now proceed to a further examination 

1 Bosanquet, Logic, Vol. II. p. 118. 



TYPES OF INDUCTIVE INFERENCE 43 

of these methods, considered both singly and to- 
gether. 

1. They all proceed upon the supposition that 
what is given in consciousness has some necessary 
ground for its being. In enumerative induction, 
there is some causal connection presupposed, yet in 
a very general and indefinite manner, and accom- 
panied by no analysis of the various concepts either 
by a systematic observation or experiment. It is a 
vague sense of uniformity which, when observed for 
many times, we feel will continue indefinitely. That 
which has happened often and not contradicted car- 
ries with it a certain convincing power by dint of bare 
repetition, especially to persons of narrow experi- 
ence, and unaccustomed to discriminating observa- 
tion. Ueberweg has made the following comment in 
reference to the so-called imperfect induction. " The 
conclusion is made universal with more or less prob- 
ability, and the blank which remains over in the 
given relations of spheres is legitimately filled up 
partly on the universal presupposition of a causal- 
nexus in the objects of knowledge, partly on the 
particular presupposition that in the case presented 
such a causal-nexus exists as connects the subject 
and predicate of the conclusion. The degree of prob- 
ability of the inductive inference depends in each 
case on the admissibility of this last presupposition, 
and the various inductive operations, the extension 
of the sphere of observation, the simplification of the 
observed conditions by successive exhaustion of the 
unessential, etc., all tend to secure its admissibility." 1 
1 Ueberweg, Logic, pp. 483 f. 



44 INDUCTIVE LOGIC 

Analogy likewise proceeds upon the assumption of 
an underlying cause among the observed phenomena, 
and this is more definitely in the foreground through- 
out the process than in that of induction by enumer- 
ation. Analogy is based upon the postulate that sim- 
ilar phenomena have similar causes ; the greater the 
agreement of the various attributes of the different 
phenomena compared, the greater will be the result- 
ant probability that causes capable of producing 
them as effects will be similar. The similarity of 
the lightning flash to the electric spark suggested 
to Benjamin Franklin the possibility that they were 
due to a like origin, and by experiment his analogical 
reasoning was actually confirmed, as is well known. 
Upon the theory that the world as it exists for us 
in knowledge forms a system to some place in which 
every phenomenon given in experience must be 
appropriately and necessarily referred, it follows, 
therefore, that a simple experience, devoid of any 
complexity of parts, may fit into several possible 
places in our world of consciousness, and remain so 
far forth indeterminate. However, a complex phe- 
nomenon, with many parts intricately connected, 
will fit into one unique place only in the system to 
which it must be referred. It is like a key that 
will fit into only one lock. The presumption, there- 
fore, is that any other phenomenon which resem- 
bles the first through much of its entire content, 
part for part, attribute for attribute, will also re- 
semble it further as regards other attributes not yet 
examined, so as it will likewise fit into the peculiar 
place in the system of knowledge to which the 



TYPES OF INDUCTIVE INFERENCE 45 

first has been found to belong. There is always a 
strong probability that agreement in spheres of great 
complexity is not a mere coincidence, but the result 
of a causal relation. One characteristic of a system, 
which we have found to be the ground of inference 
generally, is the co-ordination of like things under 
one concept. Analogy, therefore, is based upon the 
view of causal connections within the system which 
comprises the world as given in consciousness. 

In the third method, the causal relation is more 
prominent still, and the search for it characterizes 
the procedure employed. That, which in the other 
methods may exist merely as a vague impression, 
is here formulated and made the direct and sole 
object of research. 

2. The three methods in the order here presented 
show an increasing prominence given to the causal 
connection in the phenomena of experience. And 
therefore they possess a relatively increasing scien- 
tific value. As the first has only indirect reference 
to the causal connection of its facts, it is the least 
trustworthy and has no claim as a scientific method. 
It breaks down as soon as an exception is noted ; 
and is even weakened by the fact that it is con- 
stantly menaced by the possibility at least of the 
appearance of an exception. " How do we know," 
says Green, " that the instances, with the examina- 
tion of which we are always dispensing on the 
strength of the rule (that is, our generalization), 
might not be just what would invalidate it, if they 
were examined ? " 1 We may arrive at the conclu- 

i Green, Phil. Works, Vol. II. p. 282. 



46 INDUCTIVE LOGIC 

sion, based upon our observation and consequent 
record, that all sheep are white, and yet black 
sheep do occur, even in every flock, as the proverb 
has it. According to Aristotle, the proposition that 
all swans are white, was a perfectly general one, 
and yet in recent times black swans have been 
discovered in Australia. Bacon's criticism upon 
this method has become classic : " Inductio quae 
procedit per enumerationem simplicem, res puerilis 
est et precario concludit et periculo exponitur ab 
instantia contradictoria et plerumque secundum 
pauciora quam par est et exiis tantummodo quae 
presto sunt pronunciat." 1 

The validity of this method of procedure depends 
largely upon the probability of our meeting and 
noticing exceptions were they to occur. As Lotze 
puts it: "A man who never observes a place of 
public resort but once in every seven days, and that 
on a Sunday afternoon, has no right to suppose, 
because it is crowded then, that it is as crowded 
on a week-day." 2 He is here in no position to note 
the exceptions even should they occur. 

Analogy, unless confirmed by experiment, or upon 
the ground of resemblance established by a verifiable 
hypothesis, has no claim to be considered as a scien- 
tific method. There may be false analogies depend- 
ing upon surface resemblances. A child might 
conclude that oil would put out fire because it 
so closely resembles water, which he knows can ex- 
tinguish the flames. The difference between essen- 
tial and . accidental agreement between phenomena 

1 Novum Organon, i. 105. 2 Lotze, Logic, p. 343. 



TYPES OF INDUCTIVE INFERENCE 47 

can be revealed only when the underlying cause is 
ascertained. 

The third method alone has scientific worth. 
True induction must be a continued search to dis- 
cover a causal relation. 

3. The two first processes fulfil their functions 
largely as tentative and suggestive methods. In 
enumeration of instances, we are often led to note 
resemblances which become the basis of analogy. 
And analogy suggests, in turn, hypothesis which is 
capable of verification through subsequent experi- 
ment. 

The question may be put, "Which of the three 
processes is induction proper ? " The fact is that 
it may involve all three, but it is not complete until 
it reaches the third, — the experimental method. 
Analogy is especially fertile in suggestion. Scien- 
tific minds most carefully trained and versed in 
scientific methods of research are often most keen 
in noting resemblances, and detecting analogies 
which become the basis of their experiments. New- 
ton possessed that rare insight which, in spite of 
the manifest dissimilarity of the two phenomena, 
could yet discern an essential likeness between the 
fall of an apple and the gravitating force of the 
moon towards the earth. 

4. It is also to be observed that the choice of 
method will depend largely upon mental habit. 
Some minds naturally or by special training and 
surroundings are given to experiment. They have 
a testing facility and inventive capacity. Others 
naturally are susceptible in an unusual degree to 



48 INDUCTIVE LOGIC 

contrasts and resemblances. Others again are ac- 
customed to accurate observation that is ever push- 
ing beyond and seeking to extend its sphere. Thus 
we have a natural division of these methods accord- 
ing to psychical proclivities. The choice of method 
is often conditioned by the force of circumstances. 
Experiment is not alway possible. Are all crows 
black ? There is no connection between the general 
organism of the crow and its color that has thus far 
been revealed through analysis or experiment. The 
only recourse is to number instances over the widest 
possible field. We say, moreover, that Mars may be 
inhabited ; for it has an atmosphere similar to the 
earth and therefore capable of sustaining life. 
Analogy is the only guide in such a case, and it is 
impossible to verify it either by observation or 
experiment. 

5. All the methods tend to one end, that of ef- 
fecting a generalization of experience. The gen- 
eralization may be either a numerically general one, 
or one expressed in terms of a generic concept. 

(1) The former consists in the extension of several 
instances to their repetition under like conditions. 

(2) The second consists in the extension of several 
instances to all cognate species under the same 
genus. 

Examples of these two kinds of generalization 
are as follows : The general proposition that all 
sulphur is combustible is of the former kind; all 
instances are substantially of the same nature, and 
do not differ as distinguishable species under the 
same genus, but rather a repetition of like phenom- 



TYPES OF INDUCTIVE INFERENCE 49 

ena. The general concept in the above proposition 
is of the nature of an infima species. On the other 
hand, the proposition that all mammals are verte- 
brates, has the subject-term in form of a generic 
concept. Many species, differing widely among them- 
selves, may be embraced under it. 1 

i Sigwart, Logic, Vol. II. pp. 310, 311. 



CHAPTER V 

Causation 

We have seen that induction as a truly scientific 
method consists in the analytical determination of 
the relations of cause to effect in any complex phe- 
nomenon, accompanied by a generalization of the 
result obtained. The final outcome of such a proc- 
ess is an universal concept which embodies a law, 
expressed in terms of a constant connection between 
antecedent and consequent. As Green has said, 
" The essence of induction consists in the discovery 
of the causes of phenomena." 1 A causal view of 
the universe gives rise to logical concepts, whereas 
a mythological view of the universe, as in ancient 
times, resulted in mere empirical concepts, which 
gave no assurance either of stability or invari- 
ability. It will be necessary, therefore, to de- 
termine more precisely the logical significance of 
the causal idea, which seems to underlie all induc- 
tive inference. This is no easy task. According to 
Clifford, cause has sixty-four meanings in Plato, and 
forty-eight in Aristotle. 2 

i Green, Phil. Works, Vol. II. p. 284. 

2 Clifford, Lectures and Essays, Vol. I. p. 149. 

50 



CAUSATION 51 

The causal idea has sometimes found expression 
in the phrase, the uniformity of nature, or it is often 
referred to as the doctrine of universal causation. 
These two phrases are often used interchangeably ; 
this gives rise to confusion of thought, for their 
meanings are quite distinct. Uniformity of nature, 
strictly interpreted, means that like antecedents, 
under precisely the same conditions, will be fol- 
lowed by like effects ; this idea expresses one phase 
of causation, viz. its invariability. The doctrine of 
universal causation, however, expresses the impos- 
sibility of phenomena rising spontaneously, without 
an antecedent, or antecedents, sufficient rationally 
to account for them. The two ideas lie at the root 
of the causal idea. As Tennyson has put it : — 

For nothing is that errs from Law. 

Some confusion has also arisen from the failure to 
discriminate precisely between the philosophical and 
the purely logical questions relative to the general 
subject of causation. Causation may be viewed 
from three different points of view : — 

1. What it is phenomenally, that is, as regards 
its physical aspects. 

2. What it is essentially, as regards its real 
nature. This is a metaphysical question. 

3. What it is in respect to its characteristic 
attribute of invariability. This is a purely logical 
question. 

(1) As to the first, what is causation phenome- 
nally? What is its purely physical significance? 
Investigations in this line have led to the doctrine 



52 INDUCTIVE LOGIC 

of the conservation of energy. This is substan- 
tially the assertion that, in every event, no new 
energy is called forth which did not exist before, 
potentially at least, nor can any energy be ulti- 
mately lost; nothing new is created, — there is only 
a change or transfer from one state or condition to 
another. Moreover, the sum total of energy in the 
universe is a constant quantity; it can neither be 
added to, nor subtracted from. There is an excel- 
lent illustration of this theory in the admirable 
chapter on " Conservation of Energy " by Professor 
Tait. I give it somewhat in full : " I allow an 
electric current to pass through a galvanic battery 
and there is for the moment a certain quantity of 
zinc consumed, or, as we may put it, a certain quan- 
tity of potential energy in the battery has been 
converted into the kinetic energy of a current of 
electricity. That current of electricity passes round 
some yards of copper wire, coiled round a bar of 
iron or a number of fine iron wires which are stand- 
ing vertically inside this apparatus. The moment 
the current passes, these iron wires are converted 
into magnets, but, in consequence of the conserva- 
tion of energy, while this is going on they weaken 
the current. The current of electricity becomes 
weaker in the act of making the magnet, but the 
moment the magnet springs into existence, it again 
is weakened, because, from the necessities of its 
position, its mere coming into existence necessitates 
the passage of a new current of electricity in an- 
other coil of wire which surrounds this externally, 
and finally this last current we can use to produce 



CAUSATION 53 

heat, or light, or sound." J In this cycle of changes 
we see how closely connected even disparate phenom- 
ena are, and how the appearance of energy in any 
one definite state is dependent upon its previous 
existence in some other state. The doctrine of 
conservation of energy, we shall see later on, may 
be suggestive as to the nature of the analytical 
treatment of cause and effect. 

(2) The philosophical question as to the inner 
nature of causation met with one answer generally 
until the time of Hume; namely, that the idea of 
cause signified that the antecedent was efficient in 
producing the corresponding consequent, implying 
the transfer of power sufficient to bring about the 
effect. Hume, however, contended that in the 
greatest possible extent of our knowledge, all that 
we certainly know is this, that one event follows 
another. We have no ground for an assertion 
concerning the manner in which the sequence is 
effected, nor assume any real tie between them. 
Hume insisted that phenomena were conjoined, but 
never connected. 2 His opponents, as Kant and 
others, deny him, however, his fundamental posi- 
tion, — that the origin of the causal concept comes 
from experience alone. They urged that it has an 
a priori origin, a concept simple and unanalyzable, 
given through intuitive insight; developed in the 
sphere of experience, but not dependent upon expe- 
rience for its warrant. It is an interesting fact 
that the idea of the conservation of energy devel- 

1 Tait, Recent Advances in Physical Science, pp. 76, 77. 

2 Hume, Essay on Idea of Necessary Causation. 



54 INDUCTIVE LOGIC 

oped subsequent to Hume's time. It seems to give 
evidence which. Hume insisted was not and could 
not be forthcoming, namely, concerning the idea of 
the antecedent as an efficient power. Through the 
modern doctrine, the impression of a transfer of 
real power is produced, though its mode and man- 
ner still remain a mystery. 

(3) The logical aspect concerns not the phenome- 
nal manifestation of cause and effect, nor their inner 
nature, but rather the element of invariability in 
causation. Two questions here suggest themselves : 
First, Is invariability a fact, — a constant ele- 
ment in causation ? Second, How do we account 
for its existence ? The first only has truly logical 
significance. The invariability of causation, that 
like antecedents under precisely the same condi- 
tions produce like effects, alone makes induction 
possible. Mill says that it is the belief in the 
uniformity of nature which stands as the ultimate 
major premise in every process of induction. 
Hume accepted it, and based inferences upon it, 
and never challenged it as a working basis as 
regards the affairs of every-day life. He acknowl- 
edged the element of invariability, and only denied 
the bond of connection. This element has peculiar 
logical significance : without it, it would be impos- 
sible to extend our knowledge beyond the seen and 
the heard, indeed that which is seen and heard 
would then have no meaning, and no basis for their 
interpretation and appreciation. Being assumed, 
however, in our logical postulate, we have a basis 
for induction, — a constant to be sought for, and to 



CAUSATION 55 

be depended upon, in explanation of the. past and in 
prediction of the future. 

When we come to the second question, which is 
essentially a genetic one, how the belief in the uni- 
formity of nature arose, we find two classes which 
answer respectively that the belief arose a priori, 
and on the other hand, from experience simply. 
The former is the opinion especially associated with 
the Scottish School of philosophy. Hume holds 
that it proceeds from a psychological law of custom 
or habit, — an unbroken line of mental associations 
inducing a belief within, concerning the uniformity 
of nature without. Mill has also a like empirical 
basis for a belief in the uniformity of nature ; he 
holds that having observed uniformity in many 
experiences, in fact never contradicted, we general- 
ize so as to cover a sphere beyond our experience. 
Moreover, we possess the consensus of testimony, 
coextensive with the history of humanity, of the 
indefinitely wide extent of the sphere of causation, 
and the accompanying characteristic of uniformity. 
His position is fortified by the fact that in the 
process of incomplete induction, its probability is 
strengthened where there has been exceptionally 
abundant scope for observation, so that there is the 
overwhelming conviction that if there had been a 
time or place where the law would prove untrue, it 
would have been noticed. Instead of universal 
causation, Mill and his followers make a more 
cautious statement ; causation as coextensive 
with the sum total of human experience. This is 
abundantly adequate to embrace all possible cir- 



56 INDUCTIVE LOGIC 

cumstances of practical inference. The immensely 
high degree of probability engenders a subjective 
certitude which in every-day conduct of affairs, and 
even in the more exact requirements of scientific 
investigation, is never questioned. 

Preyer has given an interesting account of the 
extremely early appearance of the appreciation of 
the causal relation in the case of his child, " who, at 
the three hundred nineteenth day of its life, struck 
several times with a spoon upon a plate. It hap- 
pened accidentally, while he was doing this, that he 
touched the plate with the hand that was free ; the 
sound was dulled, and the child noticed the differ- 
ence. He now took the spoon in the other hand, 
struck with it on the plate and dulled the sound 
again, and so on. In the evening the experiment 
was renewed with a like result. Evidently the 
function of causality had emerged in some strength, 
for it prompted the experiment. The cause of the 
dulling of the sound by the hand — was it in 
the hand, or in the plate ? The other hand had 
the same dulling effect, so the cause was not lodged 
with the one hand. Pretty nearly in this fashion 
the child must have interpreted his sound-impres- 
sion and this at a time when he did not know a 
single word of his later language." 1 

The theoretical soundness of Mill's speculations, 
however, has a flaw, although the practical results 
may not be thereby invalidated. The inductive proc- 
ess, which is supposed to be a truly scientific method, 
and superior to induction by simple enumeration 
1 Preyer, The Senses and the Will, pp. 87, 88. 



CAUSATION 57 

must, according to Mill, at the last analysis, rest 
upon a principle which is itself based, upon an in- 
complete induction. A very fair and searching criti- 
cism of Mill is that of Venn's in his Empirical Logic} 
Wl lately insists that the whole question concerning 
the nature of our belief in uniformity is irrelevant, 
as it is a purely psychological and not a logical 
one. Mansel holds a mediating position in insist- 
ing that the idea of universal causation is intuitive, 
while that of uniformity is necessarily empirical. 
Sigwart has very trenchantly criticised Mill in that 
"taking away with one hand what he gives with 
the other, he shows in the uncertainty of his 
views the helplessness of pure empiricism, the im- 
possibility of erecting an edifice of universal propo- 
sitions on the sand-heap of shifting and isolated 
facts, or, more accurately, sensations ; the en- 
deavor to extract any necessity from a mere sum 
of facts must be fruitless. The only true point in 
the whole treatment is one in which Mill as a logi- 
cian gets the better of Mill as an empiricist; namely, 
that every inductive inference contains a universal 
principle ; that if it is to be an inference and not 
merely an association of only subjective validity, 
the transition from the empirically universal judg- 
ment all known A's are B to the unconditionally 
universal all that is A is B, can only be made by 
means of a universal major premise, and that only 
upon condition of this being true are we justified 
in inferring from the particular known A's to the 
still unknown ^4's." 2 

1 Veuu, Empirical Logic, p. 130. a Sigwart, Logic, Vol. II. p. 303. 



58 INDUCTIVE LOGIC 

The whole tendency of the modern logic is to 
base the causal postulate upon a ground which is 
episteniological ; namely, inasmuch as our knowl- 
edge is one and self-consistent throughout all its 
separate elements, there must be a corresponding 
invariability in the phenomena themselves, as there 
is in the system of knowledge which results from 
the interpretation of these phenomena. This is 
the general view of Sigwart, Bosanquet, Lotze, and 
Green. 1 

This view may be considered also as an expres- 
sion of the Law of Sufficient Reason ; namely, that 
there is an inherent characteristic of intelligence 
which demands that every element of conscious- 
ness must be referred to some other element for its 
explanation, and that it is only when the logical 
connection of ideas corresponds to a real causal 
connection, that the mind discovers a reason for 
its several experiences which is satisfying. It has 
been said by Ueberweg, as given expression to this 
view : " The external invariable connection among 
sense phenomena is, with logical correctness, ex- 
plained by an inner conformability to law, accord- 
ing to the analogy of the causal connection perceived 
in ourselves between volition and its actual accom- 
plishment." 2 

There is a distinction that is of importance to 
note between the popular and the scientific idea of 

1 Sigwart, Logic, Vol. II. pp. 119, 120; Bosanquet, Logic, Vol. 
II. pp. 220,221; Lotze, Logic, p. 68; Green, Phil. Works, Vol. II. 
p. 286. 

2 Ueberweg, Logic, pp. 281, 282. 



CAUSATION 59 

cause. The former is the outcome of the supposi- 
tion that whatever immediately precedes the effect 
has evidently produced it, and that this is sufficient 
wholly to account for it. Such an idea of causes 
leads, at the best, but to a loose and superficial 
determination of the relation between any ante- 
cedent and its consequent, and there is the danger, 
moreover, of a hasty inference which results in the 
fallacy of post hoc ergo propter hoc. In order to 
attain a true view of causation, we must especially 
attend to the extreme complexity of the causal con- 
nection. There is no such thing as a simple cause 
followed by a simple effect. The cause is always a 
combination of several elements, circumstances, and 
conditions; the effect is always manifold. This 
characteristic has been admirably presented in 
Mill's chapter on the " Plurality of Causes and the 
Intermixture of Effects. It is well known that the 
variation in the height of a barometer is due partly 
to the variation of the atmospheric pressure, and 
partly to the variation of the expansion of the mer- 
curial column due to heat. In exact determination, 
some experiment or calculation must precede, before 
there can be a discrimination between the elements 
of the joint effect. And so also, a number of cir- 
cumstances may combine to restore an invalid to 
health, no one of which alone being capable of 
effecting his recovery. 

The cause of any phenomenon has been defined 
by Mill, as also by Brown and Herschel, as the sum 
total of all its antecedents. This statement has 
been criticised, inasmuch as the sum total of all 



60 INDUCTIVE LOGIC 

antecedents is indeterminate, and that there is no 
end to the possible ramifications in all directions 
which an exhaustive analysis of any complex cause 
will yield. However, the problem is one of reduc- 
tion to simplest possible terms within the range of 
our powers of observation and experiment. There 
is much in the sum total of all the antecedents of 
any given effect which is irrelevant. It is the 
peculiar function of logical analysis to discriminate 
between the relevant and irrelevant. The temper- 
ature of the laboratory will not affect, one way or 
the other, experiments with falling bodies ; but will 
essentially influence certain chemical experiments, 
and must enter as one of the determining factors in 
the sum total of antecedents. It may be that cer- 
tain elements of a complex whole may seem to us 
ultimate and unanalyzable, and yet be themselves 
systems of more or less complexity. There is 
always a limit to analysis, both experimental and 
mental. The analysis is to extend to the ultimate 
parts as far as possible. It is not an exact process, 
but a process which tends to exactness to the ex- 
tent which the scope of finite intelligence will per- 
mit. The reason is not at fault so much as the 
natural limitations of observation and experimental 
analysis. The end of our research in causal analy- 
sis is to discover an invariable relation that can be 
expressed in the form of an hypothetical universal, 
— If A, then B. 

In order to effect this, the complex A must be 
separated into its parts, a, b, c, etc., and the effec- 
tive, and necessary, and indispensable element pro- 



CAUSATION 61 

ducing B must be determined. Suppose it proves 
to be a, it may be possible to subject this to further 
analysis, and reduced to simpler elements, such as 
x, y, z, etc., and x found to be the significant ele- 
ment of the real cause. Each analysis determines 
a narrower and still narrower sphere within which 
the cause lies. A man is shot. We say the bullet 
killed him ; then the driving force behind the bul- 
let; then the explosive power of the gunpowder; 
this in turn was occasioned by the combined chemi- 
cal and mechanical energy of its ingredients, where- 
by a solid is transformed into a gaseous substance 
many times its original bulk. 

Sooner or later we must reach the end of our an- 
alysis, and the investigation be necessarily checked. 
No explanation is ultimate ; we only transfer our 
point of view from a less to a more familiar sphere 
of interpretation. We do not feel the need of ex- 
plaining the very familiar ; though the most famil- 
iar is hardest satisfactorily to explain, because there 
is nothing simpler in whose terms we may para- 
phrase it. We feel this in giving a definition of 
terms whose meaning we best know, and which we 
most frequently use. Mr. Barrett, a former assist- 
ant at the Royal Institution, said of Faraday : " I 
well remember one day when Mr. Faraday was by 
my side, I happened to be steadying, by means of 
a magnet, the motion of a magnetic needle under a 
glass shade. Mr. Faraday suddenly looked most 
impressively and earnestly, as he said : ' How won- 
derful and mysterious is that power you have there ! 
The more I think over it, the less I seem to know.' 



62 INDUCTIVE LOGIC 

And yet, lie who said this knew more of it than any 
living man." * 

Although our knowledge is limited as in all cases 
of causation, however simple, nevertheless, as far 
as it goes, the several elements are related logically, 
that is, necessarily and universally. We may only 
know in part, but still we know, and the world, as 
interpreted for us in knowledge, is a world of 
invariable sequences. The process of inductive 
analysis, therefore, consists in reducing a complex 
antecedent to its ultimate parts, in order to reveal 
the element or elements in it which have caused 
the given effect. It sometimes happens that differ- 
ent elements in an antecedent may be regarded 
severally as the cause, according to the psychologi- 
cal point of view as regards the interests of the 
investigator. It is not always that a scientific 
determination of the cause is required ; it may be 
that all that is desired is a knowledge of that part 
of the antecedent which is most closely and prom- 
inently connected with the event in question. An 
inquiry may be started in reference to the cause of 
an epidemic in a community. One may discover 
the cause in the carelessness of sanitary engineers ; 
another may say the cause lies in the poor construc- 
tion of the sewerage ; another says that the cause 
of the epidemic is a certain kind of bacilli. Each 
one is looking at the chain of events related as 
cause and effect ; but they all look at different links 
of the same chain. One element, therefore, of a 
complex antecedent may be brought into more or 

1 Gladstone, Michael Faraday, p. 180. 



CAUSATION 63 

less prominence as the efficient element of the 
cause, according as the point of view is shifted. 
If, in the search for the cause of phenomena, the 
sum total of antecedents were always given exhaus- 
tively, the explanation might become so loaded 
down with details as to burden the mind and con- 
fuse, rather than clear, the understanding. 



CHAPTER VI 

The Method of Causal Analysis and Deter- 
mination 

It will be well to consider the various problems 
which will confront vis in seeking to analyze a com- 
plex antecedent for the purpose of discovering its 
cause. 

1. There are problems where cause and effect 
appear in evident sequence. There is an antece- 
dent which is followed by a consequent. If A 
happens, then B will happen. Instances of this 
kind most readily yield themselves to the process 
of analysis, because a change in any given phe- 
nomenon is occasioned by the efficiency of the ante- 
cedent which is observed in connection with the 
change itself. It is easier to note active than 
passive relations, the dynamic rather than the 
static. The attention is attracted and held by 
change. The bird flying across our path is ob- 
served, and the one perched upon the tree near 
at hand, however conspicuous may be its position, 
is passed by without any notice taken of it. It is 
easier to connect the moisture of the grass with 
falling rain, than when the same is occasioned by 
the dew. In one case, the causal relation is ex- 
64 



CAUSAL ANALYSIS AND DETERMINATION 65 

hibited in operation ; in the other, the connection 
is veiled. We find the grass wet ; what preceded 
it we are not able to see. There are several in- 
stances of sequence among observed phenomena 
which must be carefully discriminated in order to 
avoid confusion of thought. They are as follows : — 

(1) When we have A followed by B, and A 
ceases wholly while B endures for an appreciable 
time afterwards, or it may be permanently. A 
billiard ball strikes another, the second goes on 
by virtue of the newly acquired energy transferred 
by impact from the first, which, however, stops 
altogether. I throw a ball which lodges on the 
top of a building ; the effect produced lasts per- 
manently, for the ball has gained a gravity poten- 
tial due to the energy imparted to it by the initial 
throwing. The old formula, therefore, does not 
always hold : " Cessante causa cessat effectus." 

(2) Cases where A ceases, and thereiipon B 
immediately ceases also. If we cut off the supply 
of gas which feeds a flame, the flame at once dis- 
appears. There are cases, however, when an ap- 
preciable time must elapse in order that the 
transferred energy in the effect may be dissi- 
pated. When we shut our eyes the stimulus caus- 
ing the perception is cut off, and the perception 
at once is at an end ; however, there are cases 
where the stimulus being very strong, after-images 
are induced which remain for some time in the 
dark field after the eyes are closed. 

(3) Cases where the antecedent is wholly in- 
adequate to produce the effect, but whose function 



66 INDUCTIVE LOGIC 

is merely to liberate potential energy already 
stored, and waiting an occasion for its active 
manifestation. A slight blow npon a piece of 
dynamite causes an explosion wholly dispropor- 
tionate to the striking force employed. As is 
well known, heat is often an exciting cause of 
chemical action. In such cases the real cause is 
more or less concealed, while that which is appar- 
ent upon the surface is not a cause so much as an 
occasion of the phenomenon in question. I touch 
the pendulum and a clock starts and so continues for 
many hours ; the swinging pendulum, however, is 
only the occasion of liberating the potential energy of 
the wound-up spring, and thence the power which 
runs the clock, pendulum, wheels, hands and all. 

2. We have also instances not so much of se- 
quence as of concurrence. The planets revolve 
around the central sun ; here the cause is constant, 
attended by constant effect. The machine never 
runs down ; nor has to be wound up, so that it can 
be seen that the cause antedates the effect. 

3. Cases of Coexistence. — These are more diffi- 
cult to analyze, for the phenomena do not here 
appear as antecedent and consequent in the midst 
of changing conditioas and circumstances. We 
have coexistence of two kinds. 

(1) Coexisting attributes in one and the same 
organism. They are always found together. They 
form one generic concept and are called by one 
name. Cows have horns, cloven feet, are rumi- 
nant, etc. Dogs have their distinct and constant 
characteristics. The orange has its correlation of 



CAUSAL ANALYSIS AND DETERMINATION 67 

color, taste, smell. And so we have the so-called 
" natural kinds," i.e. organisms presenting an 
unique and characteristic appearance, differenti- 
ated thereby from all others. There are also 
certain correlations of growth which present a 
constant relation between certain attributes, as 
the fact, however we may explain it, that cats 
with blue eyes are invariably deaf. There are, 
moreover, illustrations of the same in an inorganic 
sphere, as the law which connects the atomic 
weight of substances and their specific heat by 
an inverse proportion ; or that other law which 
obtains between the specific gravity of substances 
in the gaseous state, and their atomic weights, 
they being either equal or the one a multiple of 
the other. In many cases, the bare fact of co- 
existence must be accepted without being able to 
explain the causal ground of it. The several ele- 
ments present a constant association, and that is 
all that can be said about it. In other cases, 
however, a cause may be found as regards, for 
instance, the correlation of warm-blooded animals 
always possessing lungs. The connection between 
respiration and the generation of heat is found to 
depend upon chemical action as its causal basis. 

(2) A relation of statics rather than dynamics, as, 
for instance, a pillar supporting a roof or arch, is 
said to be the cause in the sense of the sustaining 
cause of the superstructure. So also the cohesive 
force which holds together the particles of a stone. 
In such cases the energy inherent in the cause is of 
the nature of a stress and strain. 



68 INDUCTIVE LOGIC 

4. Under this head are embraced the phenom- 
ena of vital growth or development. These are the 
most difficult of all the causal problems to deter- 
mine ; for it is required to discover the inner neces- 
sity of essence, and how the succeeding stages of 
development unfold through the play of the central 
forces inherent in the very nature and being of the 
organism itself. Mill is content with classifying 
organisms as different natural kinds, and he is not 
concerned with the reason why there should be 
such and such kinds, nor does he attempt to discover 
any law concerning these natural correlations and the 
mode of their growth. In inductive analysis, our 
concepts must not merely grasp what the natural 
kinds are, but also what has determined them to be 
what they are. Darwin puts special emphasis upon 
the environment as affecting changes in organisms 
and producing differentiating modifications among 
species. This, however, must be considered not as 
sole factor, but one which is combined with inner 
needs and necessities. Moreover, Darwin has drawn 
attention to the fact that individual differences need 
scientific explanation as well as the common attri- 
butes, as, for instance, why some sheep are black, 
and why some pigeons are fan-tailed and others are 
not. In all such considerations we must not lose 
sight of the fact that there are two determining 
factors, — the inner necessity of development ; and 
the external necessity of causality, as organisms 
are acted upon by their environment. 1 

5. Cases of collocation where no one element of 

1 Sigwart, Logic, Vol. II. pp. 322, 330, 331. 



CAUSAL ANALYSIS AND DETERMINATION 69 

the cause is efficient, but all together they combine 
to produce the effect. In searching for the cause, 
we must not only find a certain amount of energy 
capable of producing the effect, but Ave must also 
discover what peculiar arrangement of the elements 
concerned must exist before the energy in question 
can become operative. Chalmers says that " the 
existing collocations of the material world are as 
important as the laws which the objects obey, that 
many overlook this distinction and forget that 
mere laws without collocations would have afforded 
no security against a turbid and disorderly chaos. nl 
We would naturally say that the sole cause of water 
boiling at 212° is the enveloping heat ; it has, how- 
ever, been observed that on top of Mont Blanc, 
water boils at 180° instead of 212°. This indicates 
that, in addition to the fire, the atmospheric press- 
ure is an element in the cause, very easily over- 
looked. Charcoal and diamond are of the same 
substance ; a difference only in the arrangement of 
the molecules results in such radically different 
combinations. There are, in the main, three special 
kinds of collocations, as follows : — 

(1) Cases of modifying circumstance. A strong 
wind blows down a tree ; this would not have oc- 
curred had not the tree been hollow. The hollow- 
ness of the tree is here a co-operative circumstance 
that is combined with the efficient cause, — the force 
of the wind. An instance where arrangement of 
the elements concerned rather than their efficient en- 
ergies is productive of the effect, is that of capil- 

1 Quoted by Jevons, Principles of Science, p. 740. 



70 INDUCTIVE LOGIC 

larity, the rising of liquid in a tube of exceedingly- 
small bore. Here form is more essential to the 
effect than the expenditure of any visible energy. 

(2) Cases in which certain negative conditions 
prevent the realization of the effect. The plants 
and shrubs die in a long drouth, because it did not 
rain. A train collides with another, because the 
red signal was not exposed as it should have been. 
A match will ignite gunpowder generally, but it 
fails to do so should the powder prove to be wet. 

(3) There are also cases of counteracting causes, 
where the effect of cause A is not realized, as cause 
B neutralizes the force of cause A ; as when an 
anchored boat will not respond to the pull of the 
oar. Sometimes the cause is not wholly counter- 
acted, or it may be the counteracting cause more 
than holds the positive cause in check, and is itself 
operative. The rise of a balloon in the air is due 
to the fact that the force of gravity is more than 
overbalanced by the expansive force of the gas 
within the balloon; one force pulling downwards, 
the other bearing up, and the latter prevailing. 

Mechanical forces acting in combination admit 
of a resolution of their joint effect according to 
the theory of the parallelogram of forces. Chemi- 
cal and vital forces cannot be treated in such a 
way at all. From the character of the elementary 
forces in mechanics, one can calculate their com- 
bination. In chemistry, however, when the ele- 
ments are given, the resulting compound cannot 
be thus determined. So, also, in vital and mental 
phenomena, the necessarily complex nature of the 



CAUSAL ANALYSIS AND DETERMINATION 71 

elements involved prevents not only prediction of 
resulting combinations, but even adequate explana- 
tion of that which may be immediately given in 
consciousness. 

6. It is necessary, in the investigation of causal 
relations, to understand the different modes of the 
transfer of energy, which are as follows : — 

(1) Molar or mechanical, as in the case of a 
billiard-ball transferring its energy to another 
through impact. 

(2) Molecular, as heat, chemical and electrical 
and magnetic forces, light, etc. One passes into 
another, as chemical force producing electric, elec- 
tric producing magnetic, or producing heat and 
light. 

(3) Cases where mechanical force becomes mo- 
lecular, as friction inducing heat; or cases where 
molecular becomes mechanical, as heat transferred 
into the driving power of an engine, or electricity 
applied as a motor. A precise determination of 
equivalents can be made between molar and molec- 
ular energy ; as, for example, it has been found 
that it takes the same amount of energy to raise 
772 pounds a distance, of one foot that it does to 
raise the temperature of one pound of water 1° F. ; 
or the heat requisite to boil a gallon of freezing 
water would lift 1,389,600 pounds through a dis- 
tance of one foot. 

As a consequence of the doctrine of the transfer 
of energy, a causal law can be so stated as to ex- 
press the fact that variations in the antecedents 
will call for corresponding variations in the effect, 



72 INDUCTIVE LOGIC 

as, for instance, such a law as the following : " Re- 
sistance in a wire of constant section and material 
is directly proportional to the length and inversely 
proportional to the area of the cross-section." 1 
The neglect of quantitative determination of the 
proportionate variations of the antecedent and conse- 
quent was a glaring defect in the inductive systems 
both of Mill and of Bacon. 

Through the representation of the various stages 
of such variation, it is also possible to establish the 
upper and lower limits beyond which the cause does 
not produce the corresponding effect ; as in Weber's 
law concerning the relation of stimulus to sensa- 
tion, that stimulus must increase geometrically in 
order that the sensations increase arithmetically. 
There is an upper and lower limit beyond which 
this proportion does not hold. 

The doctrine of conservation of energy creates 
the impression of continuous change in causation, 
in which the effect unfolds out of the cause. We 
do not think of phenomena under this aspect as 
discrete events. More than ever, in the light of 
modern science, does the old saying obtain, " Natura 
non facit saltum." We no longer look for catas- 
trophic results in nature — but regard causation 
as a continuous transfer of potential energy into 
kinetic or actual energy. 

We come now to the consideration of the method 
by which the causal analysis is mediated. This 
is effected through observation and experiment. 
Observation is something more than mere looking at 

1 Jenkin, Electricity and Magnetism, p. 83. 



CAUSAL ANALYSIS AND DETERMINATION 73 

phenomena; it means concentration of attention for 
the purpose of research ; it means discriminating 
insight, an appreciation of likeness and difference ; 
it means a penetration beneath surface appear- 
ances, and an apprehension of the essential features 
of the objects of perception. Experiment consists 
in modifying the elements which form the complex 
antecedent in order to observe the resultant effect 
upon the corresponding consequent. Forces may 
be added or subtracted; their intensity may be 
varied, increased, or decreased ; the circumstances 
or conditions may be altered. Herschel speaks of 
observation and experiment as passive and active 
observation. When we interfere to change the 
course of nature, or to bring natural forces within 
the range of our observation, we are experimenting. 
Observation is preliminary to experiment, and sug- 
gests the lines along which experiment should pro- 
ceed. An observation that sees the parts in the 
whole and the whole in the parts, is in itself an 
analysis of a phenomenon, in course of which proc- 
ess causal relations must be disclosed. The scien- 
tific spirit demands absolute veracity in observation. 
One ought not to be blind to facts even though they 
tend to contradict preconceived theories. Bacon 
has observed that " men mark when they hit, never 
mark when they miss." We must strive against a 
natural tendency to see things as we would have 
them, and not as they strictly are. 

We must also carefully distinguish between ob- 
served facts, and inferences which we instinctively 
draw from these facts. Observation is preliminary 



74 INDUCTIVE LOGIC 

to an inductive inference, therefore it must not it- 
self involve an inference, or we should be arguing 
in a circle. An interesting illustration of the dif- 
ference between observation and inference based 
upon it, is narrated in the life of Faraday: "An 
artist was once maintaining that in natural appear- 
ances and in pictures, up and down, and high and 
low, were fixed indubitable realities ; but Faraday 
told him that they were merely conventional accep- 
tations, based on standards often arbitrary. The 
disputant could not be convinced that ideas which 
he had hitherto never doubted, had such shifting 
foundations. ' Well,'" said Faraday, ' hold a walking- 
stick between your chin and great toe ; look along 
it and say which is the upper end.' The experiment 
was tried, and the artist found his idea of perspec- 
tive at complete variance with his sense of reality ; 
either end of the stick might be called upper, — 
pictorially it was one, physically it was the other." * 
This indicates how readily our inferences and 
observations blend, and how difficult it is to separate 
them in consciousness. De Morgan has pointed 
out that there are four ways of one event seeming 
to follow another, or to be connected with it, with- 
out really being so : — 

(1) Instead of A causing B, our perception of A 
may cause B. A man dies on a certain day which 
he has always regarded as his last through his own 
fears concerning it. 

(2) The event A may make our perception of 
B follow, which would otherwise happen without 

1 Gladstone, Michael Faraday, pp. 165, 166. 



CAUSAL ANALYSIS AND DETERMINATION 75 

being perceived. It was thought that more comets 
appeared in hot than cold summers; no account, 
however, was taken of the fact that hot summers 
would be comparatively cloudless, and afford better 
opportunities for the discovery of comets. 

(3) Our perception of A may make our percep- 
tion of B follow. This is illustrated by the fallacy 
of the moon's influence in the dissipation of clouds. 
When the sky is densely clouded, the moon would 
not be visible at all ; it would be necessary for us 
to see the full moon in order that our attention 
should be strongly drawn to the fact, and this would 
happen most often on those nights when the sky is 
cloudless. 

(4) B is really the antecedent event, but our 
perception of A, which is a consequence of B, may 
be necessary to bring about our perception of B. 
Upward and downward currents are continually cir- 
culating in the lowest stratum of the atmosphere ; 
but there is no evidence of this, until we perceive 
cumulous clouds, which are the consequence of such 
currents. 1 

There are certain natural limitations to obser- 
vation, as things too minute to be seen, too swift 
to be carefully examined; there are sounds which 
some ears can detect, while others cannot, and 
shades that some eyes cannot discriminate. There 
are effects proceeding from certain causes that are 
so slight that we fail to observe them, and yet erro- 
neously infer that they do not exist. Professor 
Tyndall has given a striking illustration of the dif- 

1 Quoted by Jevous, Principles of Science, pp. 409-411. 



76 INDUCTIVE LOGIC 

ference of auditory power in two individuals; he 
says : " In crossing the Wengern Alp in company 
with a friend, the grass at each side of the path 
swarmed with insects which to me rent the air with 
their shrill chirruping. My friend heard nothing 
of this, the insect music lying quite beyond his 
limit of audition." 1 Much has been done by in- 
ventive skill to increase our powers of observation, 
and at the same time to render them more accurate, 
as the telescope, microscope, the vernier for precise 
measurement of minute differences of magnitude, the 
chronograph for time measurements, self-registering 
thermometers, the thermopile, galvanometers, etc. 
One of the chief problems of scientific method is to 
overcome natural limitations of observation through 
mechanical devices. 

Observations on a large scale and over a consid- 
erable period of time must sometimes be taken in 
order to disclose tendencies as seen only in the 
average or the mean of the observed results. Thus 
meteorological, vital statistics, and others of a like 
kind must extend over a large area, and embrace a 
large number of instances in order to reach results 
of any value. It is known that Tycho Brahe made 
an immense number of most exact records of the 
positions of the heavenly bodies with the aid of the 
best of astronomical instruments, and these records 
afterwards became the foundation of Kepler's laws 
and of modern astronomy. 2 

The faculty for accurate observation can be in- 

i Tyndall, On Sound, pp. 73, 74. 

2 Gore, The Art of Scientific Discovert/, p. 316. 



CAUSAL ANALYSIS AND DETERMINATION 77 

creased by acquiring the habit of examining care- 
fully everything within the field of vision. We fail 
to see many things because we fall into the easy way 
of passing them by without noting their presence 
or appreciating their significance. It was said of 
Charles Darwin by his son that " he wished to learn 
as much as possible from every experiment, so that 
he did not confine himself to observing the single 
point to which the experiment was directed, and 
his power of seeing a number of other things was 
wonderful." 1 The open-eyed vision is the prime 
requisite for scientific investigation. 

The limitations of observation naturally lead to 
experiment, whose special function is to so modify 
phenomena as to bring a suspected causal element 
more prominently into notice. This can be done by 
intensifying the force in question, or by neutralizing 
all other elements in combination with it, so that 
the sole effect of this force in actual operation can 
be observed. When the cause is not a simple ele- 
ment, but a combination, then the problem is to 
vary the conditions so that but one possible com- 
bination, then another, can be operative alone, and 
note the corresponding effect. Given a certain 
number of elements, the number of possible combi- 
nations is mathematically determinate, and can be 
tried seriatim until all possibilities are exhausted. 
Venn has given a long and interesting illustration 
of this in his Empirical Logic. 2 All combinations 
need not be tried, however ; for many will be seen 

1 Life and Letters of Charles Darwin, Vol. I. p. 122. 

2 pp. 402 ff . 



78 INDUCTIVE LOGIC 

to be either impossible or irrelevant. The aim is 
to obtain an antecedent which shall consist either 
of a simple element, or a combination such that with 
its presence the effect in question is present also, 
but with its disappearance the effect is wanting. 

It is not sufficient to note merely the presence 
of an antecedent connected with a corresponding 
consequent ; scientific determination consists, in ad- 
dition, in proving the absence of the suspected cause 
in cases where the given effect is not present. This 
is called determination by negation. A proposition 
which is held affirmatively has only a vague sig- 
nificance; it must be determined within definite 
limits assigned to it by virtue of what it is not. 
Defining means to set limits to a term ; these limits 
grow out of the nature of the thing itself. The 
negative judgment marks a transition always from 
that which is indefinite and incoherent to that 
which is definite and coherent. For instance, we 
have a vague notion of chemical affinity that ele- 
ments combine to form compounds. That is the 
nucleus of our knowledge ; it grows in definiteness 
through a continuous process of limitation by nega- 
tion. We find that not all elements combine with 
each other, that they do not combine except in cer- 
tain proportions, and that even those which do in 
certain definite proportions will not combine in the 
presence of others having greater affinity, as, for 
instance, in the presence of oxygen, and so on. 
Every negative proposition established renders the 
original one more accurate. 

This may be illustrated also in the concrete, when 



CAUSAL ANALYSIS AND DETERMINATION 79 

in dissection one is tracing a nerve ; it is followed 
throughout its course by a series of negative judg- 
ments though they be unexpressed : This is not a 
nerve, but an artery ; this is not a nerve, but a vein ; 
this is not a nerve, but a filament, or shred of 
muscle, etc. So we rise through negative discrim- 
ination to a clear apprehension of an object under 
investigation. The original proposition must be 
readjusted with every new negative determination. 
It sometimes happens that the original proposition 
is completely negatived by the negative determin- 
ation, sometimes again it is confirmed. 

A proposition that has not been worked over 
through such a process has no real logical worth 
or scientific value. Therefore in the analysis of 
phenomena when the suspected cause and effect 
are combined in a proposition, it can at first be held 
only tentatively. It must be confirmed negatively, 
or else readjusted to conform to the negative re- 
quirements. Suppose we have given that A is 
followed by B as far as we have been able to ob- 
serve. We may proceed by experiment to multiply 
instances of ^4's connection with B, but still the 
causal relation is not absolutely proved. We must 
go on to show that in all cases of not-,4 there is not- 
B, or in all cases of not-J3 there is not- A Negative 
experiment produces the contrapositive, or the con- 
verse contrapositive of the proposition under inves- 
tigation, which deductively necessitates the validity 
of the original proposition. 

This is substantially Mill's method of difference, 
that if an instance in which the phenomenon under 



80 INDUCTIVE LOGIC 

investigation occurs, and an instance in which it 
does not occur, have every circumstance save one in 
common, and that one occurring only in the former ; 
the circumstance in which alone the two instances 
differ, is the effect or cause or a necessary part of 
the cause of the phenomenon. This method will 
be described later ; it is the main inductive method, 
the others being largely modifications of it. A 
negative instance which is established concerning 
relations of not-^1 and not-B, is absolutely conclu- 
sive, inasmuch as not-^4 is the contradictory of A, 
and not-B is the contradictory of B. They are 
mutually exclusive. No other possibility can be 
forthcoming, and the experimental analysis is ex- 
haustive. Professor Tyndall gives the following 
account of an experiment to determine the cause of 
resonance. " I hold a vibrating tuning-fork over a 
glass jar eighteen inches deep ; but you fail to hear 
the sound of the fork. Preserving the fork in its 
position, I pour water with the least possible noise 
into the jar. The column of air underneath the 
fork becomes shorter as the water rises. The sound 
augments in intensity, and when the water reaches 
a certain level, it bursts forth with extraordinary 
power. I continue to pour in water, the sound 
sinks, and becomes finally as inaudible as at first." 1 
Prom this it is inferred that a certain column of 
water of definite height is necessary to the produc- 
tion of the sound, for above and below the limits 
no sound is heard. This experiment also indicates 
that which is most important in causal determina- 
i Tyndall, On Sound, p. 172. 



CAUSAL ANALYSIS AND DETERMINATION 81 

tion, — a variation in cause accompanied by a vari- 
ation in effect, as also a maximum and minimum 
as regards the intensity of the sound. Experiment 
proceeds upon the supposition of the measurable- 
ness of phenomena, and seeks numerically expres- 
sible results in this regard. For instance, by 
different experiments, Tyndall proved that the 
length of the column of air which resounds to the 
fork in a maximum degree of intensity is equal to 
one-fourth of the length of the wave produced by 
the fork. 1 

The negative determination of a suspected con- 
nection of cause and effect must be precise in order 
to establish the causal relation with that degree of 
accuracy which is demanded in a truly logical and 
scientific method. Upon this point, Bosanquet has 
a very suggestive passage : " The essence of signifi- 
cant negation consists in correcting and confirming 
our judgment of the nature of a positive phenome- 
non by showing that just when its condition ceases, 
just then something else begins. The ' Just-not ' is 
the important point, and this is only given by a 
positive negation within a definite system. You 
want to explain or define the case in which A be- 
comes B. You want observation of not-_B, so that 
you are lost in chaos. What you must do is to 
find the point within ^i where A x which is B, passes 
into A 2 which is C, and that will give you the just- 
not-B which is the valuable negative instance." 2 
For example, in Professor Tyndall's experiment, the 

i Tyndall, On Sound, p. 174. 
2 Bosanquet, The Essentials of Logic, p. 134. 
a 



82 INDUCTIVE LOGIC 

significant negative instance was this, — when the 
water in the tube reached just that height when for 
the first time during the experiment no sound was 
audible. The discriminating observation that can 
mark and measure the precise point of transition 
from sound to no sound, has determined accurately 
the conditions necessary to produce the sound, and 
precisely define their limitations. 

In all observation and experiment, the following 
possibilities should be kept before the mind in order 
to avoid a hasty conclusion in reference to a seeming 
causal connection. We may think that we have dis- 
covered the relation that if there is A, then there 
must be B, and the one therefore the cause of the 
other, but it may happen that 

1. Both A and B are effects of another cause and 
are thereby related co-ordinately in reference to it. 

2. A may be merely a liberating circumstance, 
or an invariable accompaniment of B. 

3. A may not be the cause of B, but only an 
element of a complex collocation which is the 
cause of B. 

4. Each separate instance of B may so differ as 
to respond to the action of A in a manner different 
from the others. 

5. A may be related to B in a system of such a 
nature, that the system in continuously developing 
new effects causes B, as the introduction of medicine 
into an organism whose forces are themselves effect- 
ing a healing process. 

6. It is often very difficult to tell whether A is 
the cause of B, or B the cause of A, as in districts 



CAUSAL ANALYSIS AND DETERMINATION 83 

where drunkenness and poverty are prevalent, or 
cases of moral and intellectual feebleness. Which 
is the cause ? and which the effect ? In many 
cases such as these, the forces react upon each 
other, the effect tending to increase the intensity 
of the cause. 

7. The connection of A and B may be one of 
mere coincidence, and not of a causal nature what- 
soever. Newton was much impressed with the 
apparent connection between the seven intervals of 
the octave, and the fact that the colors of the spec- 
trum divide into a like series of seven intervals. 
And yet there is no causal connection that can be 
proved to exist between the two. 

The more we dwell upon these various possibilities, 
the more are we impressed with the extreme com- 
plexity in which the relation of cause and effect is 
involved. The investigator must bring to his re- 
search the spirit of patience and perseverance, as 
well as a clear vision and discriminating insight. 
Sir John Lubbock, in his observations upon the 
habits of ants, says that at one time he watched 
an ant from six in the morning until a quarter 
to ten at night, as she worked without intermis- 
sion during all that time. 1 It is to such patient 
investigators that Nature reveals her secrets. 

1 Sir John Lubbock, Scientific Lectures, p. 73. 



CHAPTER VII 

Mill's Inductive Methods — The Method of 
Agreement 

There are various methods of causal research 
which have received the name of inductive methods 
and have been especially associated with the con- 
tribution of John Stuart Mill to the history of 
logic. There are five of these methods or inferen- 
tial processes as given by Mill, and forming the in- 
tegral part of his system of induction. They are 
as follows : — 

1. The Method of Agreement. 

2. The Method of Difference. 

3. The Joint Method of Agreement and Inf- 
erence. 

4. The Method of Concomitant Variations. 

5. The Method of Residues. 

The method of agreement consists in inferring 
the existence of a causal relation, when in a num- 
ber of varying instances it is observed that the 
supposed cause is always accompanied by the phe- 
nomenon in question, as corresponding effect. The 
method of difference is the comparing of an in- 
stance where the supposed cause is present, accom- 
panied by the corresponding effect, with an instance 
84 



THE INDUCTIVE METHODS 85 

having precisely the same setting, but where the 
supposed cause is withdrawn, the effect also disap- 
pearing ; the inference of a causal relation is then 
permissible. The joint method of agreement and 
difference is the comparing of instances where the 
supposed cause is present, with similar instances 
where it is absent; if the corresponding effect is 
present in the former, and absent in the latter group 
of instances, a causal relation may be inferred. 
This differs from the method of difference, that in 
the latter the same instance, now with, and again 
without the presence of the suspected cause, is the 
subject of observation ; in the joint method it is a 
number of instances with, compared with a number 
of similar instances without, the presence of the sup- 
posed cause. The method of concomitant variations 
consists in so modifying any given phenomenon that 
the supposed cause will vary in intensity ; then a 
corresponding variation in the accompanying effect 
is evidence of a causal relation. The method of 
residues consists in the analysis of a given complex 
phenomenon, in which all elements save one of the 
antecedent are known to be related in a causal 
manner to all elements save one of the conse- 
quent ; then the residual element of the one may be 
regarded as the cause of the residual element of the 
other. 

We will now examine these methods more in 
detail. The brief outline above is intended merely 
to give a general idea of the methods, that it may 
lead to a better understanding of the more exact 
statement of their nature and characteristics. 



86 INDUCTIVE LOGIC 

The Method of Agreement. — The more precise 
statement of this method is given in the first canon 
of Mill, which is substantially as follows : — 

If two or more instances of the phenomenon 
under investigation have only one circumstance in 
common, the circumstance in which alone all the 
instances agree is the probable cause (or effect) of 
the given phenomenon, or sustains some causal 
relation to it. 

The above is based upon the causal axiom that 
the constant elements which emerge in any given 
series of similar phenomena are to be considered as 
connected in some manner with the cause of the 
phenomena ; but that the variable elements are not 
connected with the phenomena in any causal man- 
ner whatsoever. 

The method of agreement is illustrated in the in- 
vestigation of the very common phenomenon of the 
transformation of substances from the solid to the 
liquid state. What is the one circumstance which 
is always present when we consider the melting of 
such widely different substances as butter, ice, lead, 
iron, etc. ? In all instances, to whatsoever extent 
they may be multiplied, of the change from solid to 
liquid states, heat has been observed to be present, 
and is thereby indicated as the likely cause of the 
phenomenon in question. The method may be 
represented through the use of symbols which, ac- 
cording to Mill, are the capital letters to denote 
antecedents, and the smaller letters to denote cor- 
responding consequents. Let the following be a 
number of different instances with the antecedents 



THE METHOD OF AGREEMENT 87 

and consequents arranged in order, and represented 
as above indicated: — 

ABC abc 

ADE . . . ade 

AMN amn 

etc. etc. 

By inspection of such a table of instances thus 
analyzed, and symbolically represented, it will be 
readily seen that A is the only element common to 
all the antecedents, while a is the only one common 
to all the consequents. The inference, therefore, is 
that A is the cause of a. It has been objected to 
this system of representation that it artificially ar- 
ranges the elements of antecedent and consequent, 
as though there were a number of distinct cause- 
elements, each connected with a correspondingly 
distinct effect-element, and it produces the impres- 
sion that it is quite an easy matter to see how these 
causal pairs are thus separately related. 1 As nat- 
ure presents her phenomena to us, however, there 
is such complexity throughout, that the analysis 
cannot readily distribute .part to part in appropri- 
ate causal relations. To avoid such an error in 
notation, I have adopted the following symbols, 
which will be used hereafter to describe the various 
methods. Let us take C as the letter to represent 
the supposed causal element, and S, the entire set- 
ting of accompanying circumstances; let e denote 
the corresponding effect, and s the sum total of the 
attendant consequences. The causal relation will 

1 Venn, Empirical Logic, p. 411. 



88 INDUCTIVE LOGIC 

be then indicated, according to the method of agree- 
ment, as follows : — 

S +C ' . s +e 

S' -f G s' +e 

S"+C s" + e 

Here the setting changes throughout, as indicated 
by S, S', S", etc., but C remains constant in the 
antecedents ; also the corresponding setting in the 
consequents changes, as indicated by s, s', s", etc., 
but e remains constant throughout. Such a nota- 
tion does not attempt to represent just which parts 
of S cause corresponding parts of s, nor by what 
elements precisely S differs from S' and S", etc. 
It does represent, however, the difference between 
the variable and constant elements of the table of 
instances which are arranged for comparison, and 
this is the key to disclose the causal relation. 

As an example of this method, let us take the 
physical law that different bodies tend at the same 
time to absorb and to emit the same waves of light. 
It is known that every substance in burning gives 
its own lines in the spectrum analysis, sodium, for 
instance, producing a very bright line in the yellow 
portion of the spectrum in a definite locality (Line 
D, of Fraunhofer). If now, instead of burning 
sodium, we interpose the vapor of sodium in the 
path of the ray which should give a continuous 
spectrum, the phenomenon is completely reversed ; 
at the exact point where there was a bright line in 
the spectrum, a dark line now appears. Thus the 
vapor of sodium, acting as a screen, absorbs the 






THE METHOD OF AGREEMENT 89 

rays which it emits when it acts as the luminous 
source. A similar effect is observed in the case of 
vapors of iodine, of strontium, of iron, etc. ; and is 
a phenomenon, therefore, admitting of generaliza- 
tion by induction. 1 This is according to the method 
of agreement ; and we may make the following 
representation : — 

Vapor of sodium acting as a screen = S + 

" iodine " " " = S' + C 

" iron " " " = S" + C 

« strontium " " « = S'" + 

etc. etc. 

The corresponding consequents are : — 

Reversing bright sodium line to dark = S + e 

" " iodine " " = S' + e 

« " iron " « = S" + e 

" " strontium" « = S"' + e 

etc. etc. 

Therefore we have : — 

S + C s+e 

£' +C s' +e 

^" +(7 s" + e 

^'" + C s"' + e 

etc. etc. 

In this the constant C of the antecedents is the 
vapor of any substance acting as a screen ; the con- 
stant e is the reversal in each case of the bright 

1 Saigey, The Unity of Natural Phenomena, pp. 94, 95. 



90 INDUCTIVE LOGIC 

line of the substance in the spectrum to the corre- 
sponding dark line of the same. From this it is 
inferred that the vapor of any substance acting as 
a screen absorbs exactly those rays which it emits 
when it acts as the luminous source. 

It is of great importance that the instances se- 
lected for observation or experiment be as varied as 
possible, so that widely differing phenomena may 
be gathered together. Then if running through 
them all there is one common element observed 
among the antecedents, and one common element 
among the consequents, the greater the variation 
among the instances the more pronounced will be 
the significance of the constant elements. In the 
illustration given the substances which are so differ- 
ent as iron, strontium, sodium, iodine, etc., preclude 
the possibility of the resultant phenomenon de- 
scribed being due to the peculiar properties of any 
one metal, or group of metals. So many, and so dif- 
ferent in kind, are taken as to eliminate the peculiar- 
ities attached to any one in particular. In this re- 
spect, the method is one of elimination. By varying 
the instances, the non-essential is eliminated, and the 
essential, which remains as the element common to 
all, is thereby emphasized, and differentiated from 
all attendant circumstances. 

This method also is one of discrimination, of 
discerning the constant element under the various 
changing forms which it can assume, and as such it 
is similar to the logical process of the formation of 
a concept. The concept is the grasping of the 
universal element which is present through the 



THE METHOD OF AGREEMENT 91 

particular and concrete manifestations of the same. 
Through them all there is the like common element 
which is the basis of the concept itself. 80 out 
of many particular instances the mind grasps the 
elements which are common to all, and considers 
them as related in a constant and therefore causal 
manner, which has in itself the character of a uni- 
versal concept and so admits of being formulated in 
the form of a law universal, which is the end of all 
induction. 

This method, moreover, is peculiarly adapted to 
observation, the collating of a number of instances, 
rather than to experiment. Instances cannot al- 
ways be manufactured, and so it may be beyond 
the power of experiment to reproduce them. They 
can, however, always be the objects of research, 
and as such fall naturally into the field of obser- 
vation. 

The question may properly be asked at this point, 
How does this method differ from that of induction 
by simple enumeration ? The latter we have seen 
is never satisfactory because the enumeration can- 
not be complete, and may be contradicted by an 
enlarged experience. This method, however, is 
superior in that it provides for more than simple 
enumeration of instances in which the phenomenon 
in question has occurred ; there must be a corre- 
sponding analysis of the instances, accompanied by 
a discriminating insight to distinguish the essential 
from the unessential. Number of instances in- 
creases the probability that the variable elements 
have been eliminated, and enables the mind to con- 



92 INDUCTIVE LOGIC 

centrate upon the constant elements that remain 
and are thereby disclosed. 

This method primarily admits of application to 
instances where a sequence is observable ; that is, 
where antecedent can be distinguished from conse- 
quent by an appreciable time element. It is, how- 
ever, possible to apply this method to the investi- 
gation of coexistences, where it may show that either 
the coexisting elements are related as cause and 
effect, or that in some causal manner they are the 
correlated effect of some cause sufficient to account 
for them both. Many instances may be adduced 
of the prevalence of poverty and crime associated 
together. This may indicate a causal relation be- 
tween them, and yet a sequence cannot be observed 
of sufficient definiteness to indicate which is the 
cause, and which the effect. The problem is thus 
left indeterminate, with the suggestion of some 
other cause which may possibly account for them 
both. All that the method of agreement can at- 
tain, is by collecting a number of instances of di- 
verse nature to indicate that in some way at least 
poverty and crime are connected by causal ties. 
The constant coexistence of attributes in one indi- 
vidual admits of a similar treatment and similar 
results. The fact of the high coloring of male but- 
terflies in a large number of instances, in reference to 
a variety of species, indicates a constant relation be- 
tween the fact of its being a male and the possession 
of brilliant coloring. This inseparable association 
indicates a causal relation, which, however, cannot 
be more precisely determined by this method. The 



THE METHOD OF AGREEMENT 93 

full explanation of the phenomenon requires some 
supplementary hypothesis depending upon condi- 
tions not disclosed by this method, an hypothesis 
such that the high coloring has the special function 
of attracting the female butterfly and has been 
intensified and developed by natural selection. 

The method of agreement is open to criticism at 
several points, and yet it must be at the beginning 
understood that this method does not rank as a 
final method. We shall soon see that it serves 
rather as suggestive of and leading to experiments 
according to the method of difference, to corroborate 
or disprove the results which the method of agree- 
ment may have attained. The chief criticisms that 
have been made of this method may be summed up 
as follows : — 

1. The cause indicated by the method of agree- 
ment is not thereby proved to be the sole cause of 
the phenomenon in question. We may gather to- 
gether a number of varied instances where an ex- 
tensive failure of crops in the summer has caused 
hard times during the winter following. And yet 
there may be, and as a fact there are, many other 
causes which engender periods of industrial depres- 
sion. We may say, therefore, that this method is 
capable of establishing, tentatively at least, an uni- 
versal proposition of the form, All x is y ; it does 
not, however, attempt to give any indication one way 
or the other, regarding the validity of the converse, 
All y is x. Knowing the limitations of a method, 
does not by any means destroy its legitimacy as a 
method ; it rather increases its efficiency Avithin its 



94 INDUCTIVE LOGIC 

proper sphere, by the more exact knowledge as to 
the precise extent of that sphere itself. 

2. It is urged that while it is possible to recog- 
nize in most, if not in all cases, the common element 
in the several effects of similar phenomena, it is not 
so easy a matter to differentiate the common ele- 
ment in the corresponding antecedents by the sim- 
ple method of agreement alone. For instance, in 
Bacon's illustration of the investigation of the cause 
of heat, he cites such disparate phenomena as the 
sun's rays, friction, combustion, etc. The element 
of heat is readily discernible through them all; 
but what is the common element which operates as 
cause in each case? There is the difficulty. Sig- 
wart illustrates this in the case of the phenomenon 
of death. The effect can be easily detected as sim- 
ilar throughout, but in all the antecedents the only 
property common to them all is life, and, therefore, 
we are led into the fallacy of attributing to life 
the cause of death. 1 We must therefore acknowl- 
edge that some phenomena may occur in such a 
variety and such a number of manifestations as to 
disguise the nature of the cause under the mask 
of a generality too indefinite to be recognized. In 
all such instances, the method of agreement must 
operate upon suggestions received from some other 
source, as to the nature of the common element in 
the antecedents. Or, some minor circumstances 
attending the effect may indicate more precisely 
the nature of the cause, as, for instance, the peculiar 
symptoms associated with death by drowning. 

1 Sigwart, Logic, Vol. II. p. 311. 



THE METHOD OF AGREEMENT 95 

3. The common element in the antecedents may 
prove to be an unessential accompaniment of all the 
instances examined. Its presence, therefore, may 
have nothing whatsoever to do with the observed 
effects. A number of different medicines, for ex- 
ample, may produce a certain effect alike in all 
instances. The only common element that can be 
detected in the various medicines examined, may 
be the alcohol which is used as the common vehicle 
of the different drugs, and yet its effect may be 
entirely inert as regards the medicinal qualities in 
question. The common element really efficient may 
be overlooked, and another common element which 
is easily discernible may nevertheless remain wholly 
inoperative. This difficulty may be overcome by a 
more thorough analysis of the phenomena observed, 
which may be attained by a judicious variation of 
the instances, so as to reveal, in turn, the precise 
effect of the various simple elements which together 
constitute the complex whole of the phenomenon in 
question. The defects of the method in this respect 
are, in a word, the defects of induction by simple 
enumeration. 

4. The cause may be present in all the antece- 
dents, and, notwithstanding the corresponding ef- 
fect, not appear, and this, not because the two are 
not related in a causal manner, but because the 
cause is neutralized by the associated elements 
which appear in combination with it in the various 
antecedents. For instance, diphtheria germs are the 
cause of diphtheria, and have been found accompa- 
nying this disease in all cases which have been ob- 



96 INDUCTIVE LOGIC 

served. And yet their presence is often noted when 
the disease itself does not develop. The tendency 
existing is counteracted by the condition of the 
organism at the time, so that the dread bacilli are 
inoperative and therefore harmless. As we have 
seen before, the presence of the effect necessitates 
the presence of the corresponding cause ; but by no 
means is it always true, that the presence of the 
cause necessitates the effect. The cause always 
produces the tendency at least, which, however, may 
be neutralized. 

5. This method is often applied in a very care- 
less way to the observations of persons who do not 
possess the power of accurate discrimination, and 
therefore observed coincidences are hastily assumed 
to be particular instances of an universal law. 
Such procedure leads to superstition and prejudice. 
It not only warps the judgment, owing to its illogi- 
cal nature, but it also affects indirectly the man's 
moral view, as it implies a weakness in character 
as well as in mind. This criticism refers, however, 
to the abuse rather than the legitimate use of 
this method under such restrictions as have been 
already indicated. 

The chief function of this method is that of sug- 
gestion. It indicates often only the possibility of 
the existence of a causal relation ; in other cases it 
leads to an inference of high probability. In all 
cases, however, it marks but the preliminary steps 
of an investigation which should be followed up by 
painstaking experiment. As it is the method of 
observation chiefly, it is natural that it should pre- 



THE METHOD OF AGREEMENT 97 

cede experiment ; for it is only by reflection upon 
our observations that we discover the nature and 
relations of phenomena, which serve as data for 
subsequent experiment. 

I have selected several illustrations to indicate 
the various fields of research in which this method 
of agreement has led to satisfactory results. 

The first refers to the relation between the 
occurrence of financial crises and the prevalence 
of over-production. Guyot, in his Principles of 
Social Economy, gives the following instances : 
An enormous consumption of capital in the United 
States in the seventies for the construction of rail- 
roads, was followed by unusual commercial depres- 
sion. Then the like outlay in India for railway 
construction by means of loans and taxes which 
absorbed the whole circulating capital of the Indian 
population, was folloAved by a devastating famine 
and general commercial paralysis. Again in Ger- 
many there was an enormous consumption of capi- 
tal in forts and armaments and general military 
equipment, bringing on the crisis of 1876-1879. 
England at the same time was unduly supplying 
circulating capital to the United States, Egypt, 
and her colonies, and a financial crisis Avas the 
result. Through all these varying instances and 
others of a like nature which might be added, the 
constant relation of over-consumption in the ante- 
cedents to the industrial depression evident in the 
effect, indicates the one to be the cause of the other, 
either in whole or in part. 

Again, it is narrated in Brewster's Treatise on 



98 INDUCTIVE LOGIC 

Optics that he accidentally took an impression from 
a piece of mother-of-pearl in a cement of resin and 
beeswax, and, finding the colors repeated upon the 
surface of the wax, he proceeded to take other 
impressions in balsam, fusible metal, lead, gum 
arabic, isinglass, etc., and always found the irides- 
cent colors the same. His inference was that the 
form of the surface is the real cause of such color 
effects. 1 The common element which appears in 
all the antecedents is evidently the same form 
impressed upon each, which was originally received 
from the mother-of-pearl. The cause is, moreover, 
independent of the nature of the substance in each 
case which received the impression upon its sur- 
face, because such a variety of substances was 
chosen as to eliminate the individual nature of each 
as an influencing factor in the result. In this 
experiment we see the advantage of varying the 
instances as far as possible for this very purpose of 
eliminating all irrelevant elements. Similar experi- 
ments have proved like results in reference to the 
colors exhibited by thin plates and films. Here 
the rings and lines of color have been found to be 
nearly the same whatever may be the nature of the 
substance. A slight variation in color is due to 
the refractive index of the intervening substance. 
With the exception of this, the nature of the sub- 
stance is not operative in producing the color effect, 
but the form alone. 

The celebrated scientist, Pasteur, in the year 
1868 was carrying on his investigations as to the 

1 Quoted by Jevons, PHnciples of Science, p. 419. 



THE METHOD OF AGREEMENT 99 

cause of the blight then devastating the silkworms 
of France. One of his experiments consisted in 
selecting thirty perfectly healthy worms from moths 
that were entirely free from the corpuscles, which 
latter are the germs of disease, or at that time sus- 
pected to be the germs of disease. Then, rubbing 
a small corpusculous worm in water, he smeared 
the mixture over the mulberry leaves. Assuring 
himself that the leaves had been eaten, he watched 
the consequences day by day. One after the other 
the worms languished ; all showed evidences of 
being the prey of the corpusculous matter, and 
finally, within one month's time, all died. Pas- 
teur's inference naturally was that the corpuscles 
had produced the death. Of course his results 
were not founded upon this experiment alone, but 
other experiments, carried on in many different 
ways, served to corroborate the Causal relation 
which the experiment just described had suggested 
as at least highly probable. 

In medicine also the method of agreement is 
often used with effect. Certain drugs are adminis- 
tered in a number of cases and the results noted. 
An uniform effect consequent upon the administra- 
tion of a given drug indicates a causal connection 
capable of generalization. Not only are subjects in 
disease, but also in health, selected, and the effects 
upon both the normal and morbid natures compared. 
Thus a variation in instances is secured. If a num- 
ber of different drugs produce like effects, the ques- 
tion at once suggests itself, What is the property 
common to them all? The method of agreement 



UfC. 



100 INDUCTIVE LOGIC 

often gives some indication of this, when the elim- 
ination of the inert properties can be accomplished 
through a sufficient variation of instances. The 
difficulty lies, however, in this very thing, to so 
vary the instances as to disclose the efficient ele- 
ment present in them all. Various medicines pre- 
sent a complex nature of such a character that it 
is extremely difficult to ascribe the precise effects 
which the several component parts individually 
exercise. 

The method of agreement is also used, perhaps 
unconsciously, in the conduct of the every-day 
affairs of life. Whenever different phenomena in 
our experience present certain characteristics of a 
constant nature, we are at once led to suspect a 
causal connection, and to start upon a more search- 
ing investigation of the same. Too often, however, 
the supplementary investigation is omitted, and the 
mind rests content with a few surface resemblances 
that lead to a hasty generalization, without being 
more precisely and adequately determined. 



CHAPTER VIII 
The Method of Difference 

The method of agreement, as we have seen, pre- 
sents a causal relation as a suggestion, admitting of 
a high degree of probability it may be, but requir- 
ing to be tested by some more scientific method. 
This is accomplished by the method of difference. 
Here a phenomenon is observed, in which the 
supposed cause-element and effect-element appear ; 
then while all other circumstances and conditions 
remain unaltered, the supposed cause-element is 
withdrawn, or its force adequately eliminated ; the 
immediate disappearance of the supposed effect- 
element consequent upon this, indicates a causal 
relation existing between the two. Or the experi- 
ment may be made in a different manner, but to 
the same end ; that is, a phenomenon may be char- 
acterized by the absence of both cause-element and 
effect-element; then, if the introduction of the 
cause-element does not disturb the phenomenon in 
question, except immediately to produce the effect- 
element, the inference may be drawn that the one 
is the veritable cause of the other. 

Canon of the Method of Difference. — If an in- 
stance in which the phenomenon under investigation 
101 



102 INDUCTIVE LOGIC 

occurs, and an instance in which it does not occur, 
have every circumstance, save one, in common, that 
one occurring only in the former, the circumstance 
in which alone the two instances differ is the effect, 
or it may be the cause, or a necessary part of the 
cause, of the phenomenon. 

This method has manifold illustration in our 
every-clay inferences. A person is asleep in the 
room with us, and we hear the loud noise of a slam- 
ming door, and observe the person at once awakening 
with a start and exclamation. We have no hesitancy 
in ascribing the awakening to the noise immediately 
preceding it. We observe again some one receiving 
a letter or telegram, and immediately upon opening 
it the face grows white with anxiety and fear, the 
hands tremble, and there are shown general symp- 
toms of perturbation. The message received, we 
say, has caused the mental shock and physical 
accompaniments. 

Or, taking a simple experiment in quite another 
sphere, it was observed by Boyle, in 1670, that an 
extract of litmus was immediately turned red by 
the introduction of an acid. This subsequently 
became a test for the presence of acids, the infer- 
ence being that an acid has this capacity of chang- 
ing the litmus to a red color from its original blue. 

Professor Tyndall describes an experiment to 
prove that waves of ether issuing from a strong 
source, such as the sun or electric light, are compe- 
tent to shake asunder the atoms of gaseous mole- 
cules, such as those of the sulphur and oxygen 
which constitute the molecule of sulphurous acid. 



THE METHOD OF DIFFERENCE 103 

He enclosed the substance in a vessel, placing it in 
a dark room, and sending through it a powerful 
beam of light. At first nothing was seen; the 
vessel containing the gas seemed as empty as a 
vacuum. Soon, along the track of the beam, a 
beautiful sky-blue color was observed, due to the 
liberated particles of sulphur. For a time the blue 
grew more intense ; it then became whitish ; and 
from a whitish-blue it passed to a more or less per- 
fect white. Continuing the action, the tube became 
filled with a dense cloud of sulphur particles which, 
by the application of proper means, could be ren- 
dered visible. 1 In this series of continuous changes, 
we find the one antecedent, giving initiative causal 
impulse, to be the beam of light. It was the one 
element introduced which started the several 
changes leading to the appearance of the sulphur 
visibly manifested. The one, therefore, is to be 
regarded as the cause of the other. 

It is possible to represent this method by means 
of symbols in a manner similar to that of the 
method of agreement. Let C be the supposed 
cause and e the effect corresponding, while S and s 
denote the setting ©f antecedent and consequent 
respectively. We have, therefore, the following : — 

S + C s + e 

Then, withdrawing C, we have the absence of e. 

S s 

The inference then is that C is the cause of e. 

1 Tyndall, Use and Limit of the Imagination in Science, p. 33. 



104 INDUCTIVE LOGIC 

In the method of agreement, a number of in- 
stances were taken agreeing only in the posses- 
sion of two circumstances, — the cause and effect 
elements common to them all. In this method, 
only two instances are taken, and they must be 
precisely alike, with the one exception, — the pres- 
ence of two circumstances in one, that is, the 
cause and the effect elements, and the absence of 
the same in the other. In the method of agree- 
ment, we compare the various phenomena, to note 
wherein they agree ; in the method of difference, 
we compare the two phenomena, to note wherein 
they differ. The logical axiom underlying the two 
methods is substantially one and the same, differ- 
ing only in its special adaptation in each case. 
The method rests on the assumption, which must 
be accepted as a fundamental postulate, that what- 
ever can be eliminated from the various instances- 
is not connected with the phenomenon under in- 
vestigation in any causal manner ; and the method 
of difference is based on the postulate that what- 
ever cannot be eliminated is connected with the 
phenomenon by a causal law. 

The method of difference is evidently the method 
by negation, which has already been indicated as 
the truly scientific process in induction. It is also 
pre-eminently the method of experiment rather 
than observation ; for the withdrawal or introduc- 
tion of forces can only be accomplished at will 
when we bring the phenomena under experimental 
control. At times, Nature herself may perform 
the experiment for us, and we stand simply as 



THE METHOD OF DIFFERENCE 105 

observers to note the results. This is especially 
the case in the catastrophic phenomena, such as 
volcanic eruption, earthquakes, etc. Generally 
speaking, however, the method of difference is the 
process of man's manipulation to secure purposed 
results in which a causal relation is disclosed. 

A question naturally suggests itself, What is there 
to determine the precise mode of experiment ? We 
may have given a concrete whole of extreme com- 
plexity. In our experiment, which element shall 
we proceed to eliminate, in order to note the re- 
sult ? An answer may be given us through sug- 
gestions received from the results of the method 
of agreement which has been already applied to 
the problem. If it is not possible to avail one's 
self of this contribution from another sphere of in- 
vestigation, then the complex whole must be broken 
up, as far as possible, into its simplest component 
parts, and one after another these parts, singly, 
then in pairs, and all other possible combinations, 
caused to be withdrawn, or their force neutralized, 
and the results in each case noted, as to whether the 
effect under investigation disappears. The exhaus- 
tion of all possible combinations must yield some 
definite result. Suppose, for instance, there is a 
complex antecedent involving four separable ele- 
ments, as A, B, C, D. Withdraw severally A, B, 
C, and D, noting results; then withdraw, in turn, 
AB, AC, AD, BC, BD, CD, that is, the pos- 
sible combinations of four elements taken two at 
a time ; then withdraw ABC, then BCD, ABD, 
and ACD, that is, combinations of four elements 



106 INDUCTIVE LOGIC 

taken three at a time. By such a process there 
will be disclosed whether one element alone or 
whether a combination of two or more have pro- 
duced the effect under investigation ; also whether 
more than one element or combination of elements 
may have caused the effect. 1 The practical diffi- 
culty in separating the elements of a complex 
whole, and withdrawing the several combinations 
from the whole, renders this process in many cases 
impossible. The cause, however, is generally sus- 
pected. It may be suggested by the method of 
agreement, by analogy, or by that insight which at 
once declares certain combinations to be impossible 
and others irrelevant. There is generally a mental 
experiment in which the judgment rejects unlikely 
combinations, thus narrowing the field of investiga- 
tion as preliminary to the experiments proper. 

The method of difference is open to various criti- 
cisms ; the most important are the following : — 

1. In applying this method, we may be so easily 
misled, in supposing our two instances are precisely 
alike, with the one exception of the presence or 
absence of the supposed cause, and yet in reality 
the instances may differ radically, and yet we may 
be unable to detect this. A patient may have 
medicine administered to him, and begin at once 
rapidly to recover, and yet the very taking of the 
medicine in itself may have made such a mental 
impression, inducing confidence and hope, that the 
real cause of the recovery may be due wholly to 

1 This process has heen illustrated and criticised at length in 
a striking manner by Venn, Empirical Logic, pp. 401 ff. 



THE METHOD OF DIFFERENCE 107 

this mental reaction. Persons taking pills com- 
posed of inert substances have often given evidence 
of bodily effects wholly impossible to trace to the 
medicine itself. And yet this criticism is one of 
caution rather than of censure ; for the defects are 
but difficulties which extreme care and insight may 
overcome. 

2. It has been objected that this method may 
point out the cause in the concrete instance before 
the experimenter, but that this furnishes no basis 
whatsoever for a wider generalization that the effect 
in question is always produced by this cause. Sig- 
wart has illustrated this objection by the instances 
in which typhus fever has been traced to the drink- 
ing of impure water. 1 The causal relation may be 
fully established in the cases investigated, but the 
universal proposition does not follow that wherever 
typhus fever appears, impure water has been drunk. 
This objection applies especially to cases of extreme 
complexity, where proximate causes alone can be 
discovered, and their ultimate nature, which may 
appear in various forms, is not revealed ; for in- 
stance, the impure water is not in itself the ultimate 
cause of the typhus fever. It contains the poison 
germs, the real cause; they may be introduced into 
the system in some other way. Care, therefore, 
should be taken to reveal the cause in and by itself, 
and not the cause of the cause. The objection, 
therefore, may be in a measure overcome. To 
effect a generalization, moreover, of logical valid- 
ity, it is necessary to supplement the method of 

i Sigwart, Logic, Vol. II. p. 420. 



108 INDUCTIVE LOGIC 

difference by hypothesis and subsequent verifica- 
tions, which will be described later on. 

3. This method may lead to error in cases where 
the supposed causal element is regarded as the 
cause in its entirety, when it is in reality but a part 
of the cause. If one should plant seed in a garden 
and water only one half of the plot, and it should 
follow that only the watered part brought forth the 
leaf and flower, then an inference according to 
the method of difference might be drawn that the 
water caused the sprouting of the young plants. 
And yet it must be regarded simply as contributory 
to the real cause. Such a difficulty may be obvi- 
ated by a careful discrimination in the analysis of 
the phenomenon investigated. 

4. Sometimes a liberating cause may be revealed 
by a strict interpretation of the method of differ- 
ence, when the real cause is more obscure, and may 
be overlooked. A stone may strike a can of dyna- 
mite and the explosion which occurs may be traced 
to the impact of the stone. It is the one element 
of difference introduced in the sphere of the ob- 
served phenomena, with the consequent result. 
The force existing as a potential is naturally ob- 
scure, and apt to elude observation. Therefore, 
whenever a cause disclosed by the method of dif- 
ference seems to be out of all proportion to the 
effect, it at once suggests the probability that a 
potential force not discerned by our powers of ob- 
servation has been the real cause, and the former 
a conditioning cause merely. Another illustration 
of this is the experiment of Priestley which led to 



THE METHOD OF DIFFERENCE 109 

his discovery of oxygen in 1774. He placed some 
oxide of mercury upon the top of quicksilver in 
an inverted glass tube filled with that metal and 
standing in mercury ; he then heated the oxide by 
means of a glass lens and the sun's rays, and ob- 
tained a gas, which he called " nitrous air," after- 
wards designated as oxygen. The heat in this case 
was the sole element of difference between the two 
instances, one in which there was no gas, and the 
second after application of the heat, when the gas 
was present. Here the heat must be regarded as 
the liberating and not in any sense the producing 
cause. Again, as Lotze says, "the fact that with 
the destruction of a single part of the brain a defi- 
nite psychical function ceases, is no proof that just 
this single part was the organ which alone pro- 
duced that function." 1 

In addition to the difficulties attending this 
method which have been enumerated and which 
have to do with the logical theory of the method, 
there are also difficulties of a practical nature which 
arise in the actual application of this method in ex- 
perimental inquiry. They are as follows : — 

1. Care must be taken that, in the two phe- 
nomena compared, with and without the supposed 
cause, there shall not be an interval of time elaps- 
ing, in which period some other cause might be 
introduced unknown to the investigator, and yet 
capable of producing the result, or else of neutraliz- 
ing some force that is present and itself capable of 
producing the result. For instance, if a chemical 

l Lotze, Logic, p. 322. 



110 INDUCTIVE LOGIC 

compound be left for an appreciable time, we may 
notice certain changes and be able to assert posi- 
tively that no new element has been introduced, 
and yet the action of the air may in itself have 
been sufficient to work these changes. When the 
two phenomena to be compared can be presented 
for inspection simultaneously, this difficulty is obvi- 
ated. This is illustrated in an experiment devised 
to exhibit the presence of light effects in the 
spectrum beyond the violet rays; that is, beyond 
the place where the spectrum seems to end. A 
sheet of paper is taken, the lower part of which is 
moistened with a solution of sulphate of quinine, 
while the upper part remains dry. Let the image 
of the solar ray fall upon this sheet ; the spectrum 
preserves at the top of the sheet in the dry portion 
of the paper its ordinary appearance, while in the 
moistened portion a brilliant phosphorescence ap- 
pears beyond the region of the violet rays. Here 
the dry and wet portions are simultaneously pre- 
sented, and there is but one point of difference be- 
tween the two. The inference, therefore, is readily 
drawn that the solution of sulphate of quinine is a 
substance sensitive to the ultra-violet portion of the 
sun's rays, the phosphorescence being the effect of 
these rays upon the solution. 

2. Extreme care must be taken that, in the with- 
drawing of any element in the course of the experi- 
ment, no other element is inadvertently introduced, 
and that, in adding any element, no existing element 
or combination of elements is destroyed, or their 
effect neutralized. Mr. Venn has admirably illus- 



THE METHOD OF DIFFERENCE 111 

tratecl this difficulty, and I give the following 
quotation in full from him : " We suppose that 
when we have put a weight into one pan of a pair 
of scales we have done nothing more than this, or 
can at any rate by due caution succeed in doing 
nothing more. But if we exact the utmost rigidity 
of conditions, we easily see that we have done a 
great deal more. Our bodies are heavy, and there- 
fore the mere approach to the machine has altered 
the magnitude and direction of the resultant attrac- 
tion upon the scales. Our bodies are presumably 
warmer than the surrounding air ; accordingly, we 
warm and therefore lighten the air in which the 
scales hang, and if the two scales and their con- 
tents are not of the same volume, we at once alter 
their weight as measured in the air. Our breath 
produces disturbing currents of air. Our approach 
affects the surface of the non-rigid floor or ground 
on which the scales stand, and produces another 
source of disturbance, and so on through the whole 
range of the physical forces." ' 

In the Report of the British Association, 1881, an 
account is given of Professor G. H. Darwin's exper- 
iments to measure the lunar disturbance of gravity 
at the Cavendish Laboratory by means of an ex- 
tremely delicate pendulum. It Avas found that 
approaching the pendulum in order to observe its 
reading, the surface level of the stone floor on 
which the instrument stood was deflected by the 
weight of the observer. As he stood to take the 
reading, the shifting of his weight from one leg to 

1 Venn, Empirical Logic, p. 416. 



112 INDUCTIVE LOGIC 

the other was perceptible ; so it became necessary 
to observe the reading by a telescope from a dis- 
tance, or to adopt some similar plan. 1 

Faraday was able at will to produce or remove 
a magnetic force, through the revealed properties 
of the electromagnet. Many of his experiments 
would have been impossible if it had been neces- 
sary to remove a cumbersome magnet and reinstate 
it again and again in his experiments. The electro- 
magnet, however, could produce or destroy the 
presence of magnetic force without any incidental 
perturbations. Thus Faraday was enabled to prove 
the rotation of circularly polarized light by the 
fact that certain light ceased to be visible when 
the electric current of the magnet was cut off, 
and instantly reappeared when the current was 
re-established. Faraday says of the experiment 
himself: -'These phenomena could be reversed at 
pleasure, and at any instant of time, and upon any 
occasion, showing a perfect dependence of cause 
and effect." 2 

3. In some cases it is impossible to remove an 
element which is supposed to be the cause of an 
effect under investigation. Its removal might cause 
the destruction or the impairing of the whole phe- 
nomenon. The force, therefore, that cannot be 
eliminated must be neutralized by an equal and 
opposing force. For instance, the force of gravity 
cannot be eliminated; it must, therefore, be coun- 
terbalanced by some device of the investigator. 

1 Quoted by Venn in Empirical Logic, p. 419. 

2 Experimental Researches in Electricity, Vol. III. p. 4. 



THE METHOD OF DIFFERENCE 113 

In chemistry the removal of an element from a 
compound may be impossible without destroying 
utterly the compound itself; in such a case, also, 
a neutralizing agent must be introduced. Darwin 
wished to prove that the odor of flowers is attrac- 
tive to insects irrespective of the attraction of 
color. He therefore covered certain flowers with 
a muslin net, which still attracted the insects to 
them. 1 

The following illustrations may serve further 
to exhibit the various features of the method of 
difference : — 

Mr. Robert Mallet gives the following interesting 
account of his visit to Faraday : " It must be now 
eighteen years ago when I paid him a visit, and 
brought some slips of flexible and tough Muntz's 
yellow metal, to show him the instantaneous 
change to complete brittleness with rigidity pro- 
duced by dipping into pernitrate of mercury so- 
lution. He got the solution and I showed him 
the facts ; he obviously did not doubt what he 
saw me do before and close to him ; but a sort 
of experimental instinct seemed to require he 
should try it himself. So he took one of the 
slips, bent it forward and backward, dipped it, 
and broke it up into short bits between his own 
fingers. He had not before spoken. Then he 
said, ' Yes, it is pliable, and it does become in- 
stantly brittle.' " 2 Here the experiment with and 
without the significant antecedent and consequent 

1 Darwin, Cross and Self Fertilization, p. 374. 

2 Gladstone, Michael Faraday, p. 175. 



114 INDUCTIVE LOGIC 

result indicates the causal relation, especially as 
the instantaneous effect precludes the possibility 
of the operation of any other cause. 

Another experiment of Faraday's is that of his 
investigation of the behavior of Lycopodium pow- 
der on a vibrating plate. It had been observed 
that the minute particles of the powder collected 
together at the points of greatest motion, whereas 
sand and all heavy particles collected at the nodes, 
where the motion was least. It occurred to Fara- 
day to try the experiment in the exhausted re- 
ceiver of an air pump, and it was then found that 
the light powder behaved exactly like heavy pow- 
der. The inference was that the presence of air 
was the condition of importance, because it was 
thrown into eddies by the motion of the plate, 
and carried the Lycopodium powder to the points 
of greatest agitation. Sand was too heavy to be 
carried by the air. 1 

Sir John Lubbock gives an account of experi- 
ments performed upon insects to prove that the 
sense of smell is in some way connected with 
their antennae. One experiment was performed 
by Forel, who removed the wings from some blue- 
bottle flies and placed them near a decaying mole. 
They immediately walked to it, and began licking 
it and laying eggs. He then took them away, and 
removed the antennae, all other circumstances re- 
maining the same as before, after which, even 
when placed close to the mole, they did not ap- 
pear to perceive it. Another experiment similar 

1 Jevons, Principles of Science, p. 419. 



THE METHOD OF DIFFERENCE 115 

to this was tried by Plateau, who put some food 
of which cockroaches are foud on a table and 
surrounded it with a low circular wall of card- 
board. He then put some cockroaches on the 
table ; they evidently scented the food, and made 
straight for it. He then removed their antennae, 
after which, as long as they could not see the 
food, they failed to find it, even though they 
wandered about quite close to it. 1 

Another experiment is that of Graber to prove 
the sense of hearing in insects. He placed some 
water-boatmen (Corixa) in a deep jar full of water, 
at the bottom of which was a layer of mud. He 
dropped a stone on the mud, but the beetles, which 
were reposing quietly on some weeds, took no 
notice. He then put a piece of glass on the mud, 
and dropped a stone on to it, thus making a noise, 
though the disturbance of the water was the same 
as when the stone was dropped on the mud. The 
water-boatmen, however, then at once took flight. 2 

An illustration of the method of difference occurs 
in the so-called blind experiments, which are often 
made in chemistry especially. As Professor Jevons 
has described such an experiment : " Suppose, for 
instance, a chemist places a certain suspected sub- 
stance in Marsh's test apparatus and finds that it 
gives a small deposit of metallic arsenic, he cannot 
be sure that the arsenic really proceeds from the 
suspected substance ; the impurity of the zinc or 

1 Lubbock, On the Senses, Instincts, and Intelligence of Ani- 
mals, p. 45. 

2 Lubbock, On Senses, etc., p. 75. 



116 INDUCTIVE LOGIC 

sulphuric acid may have been the cause of its ap- 
pearance. It is therefore the practice of chemists 
to make what they call blind experiments, that is, 
to try whether arsenic appears in the absence of the 
suspected substance. The same precaution ought 
to be taken in all important analytical operations. 
Indeed it is not merely a precaution, it is an essen- 
tial part of any experiment. If the blind trial be 
not made, the chemist merely assumes that he 
knows what would happen." 1 

1 Jevons, Principles of Science, p. 433. 



CHAPTER IX 

The Joint Method of Agreement and Dif- 
ference 

It has already been shown that the method of 
difference is sometimes not available, inasmuch as 
it may be neither possible nor practicable to remove 
from the phenomenon to be investigated the sus- 
pected causal element without destroying the phe- 
nomenon itself. Sometimes, too, it is impossible 
even to neutralize the effect of the causal element 
if it is allowed to remain as an integral part of the 
phenomenon. This is especially the case in all 
vital phenomena, and also in many chemical phe- 
nomena. Therefore another method is resorted to, 
which is known as the joint method of agreement 
and difference. Inasmuch as the suspected causal 
element cannot be removed, we must select another 
phenomenon as much like the former as possible, 
which is, however, characterized by the absence of 
the causal element. By the simple method of dif- 
ference, two instances only need be compared, the 
one with and the other without the causal element, 
but agreeing precisely in every other particular. 
In the joint method, the instances with and without 
117 



118 INDUCTIVE LOGIC 

the causal element, differ it may be in several par- 
ticulars. A number of varying instances must 
therefore be selected so as to eliminate the possi- 
bility of any of these differing characteristics being 
the cause in question. Therefore two sets of in- 
stances are collected, and compared. The one set 
comprises all the positive instances having the pres- 
ence of the supposed causal element, and the second 
set consists of the negative instances having the 
supposed causal element absent altogether. The 
validity of the method depends upon the similarity 
of the two sets of instances. As the similarity 
increases, the method approximates to the simple 
method of difference. 

The Canon of the Joint Method. — If several 
instances in which the phenomenon occurs have 
only one circumstance in common, while several 
instances in which it does not occur have nothing 
in common save the absence of that circum- 
stance; the circumstance in which alone the two 
sets of instances differ, is the effect, or cause, or a 
necessary part of the cause, of the phenomenon. 

The symbolical representation of this method 
may be exhibited as follows, using a similar nota- 
tion to that employed in the previous methods : — 

I. Table of positive instances. 

S +G s+e 

S' +0 s' +e 

S"+C s" +e 

S'"+C ....... s'"+e 

etc. etc. 



METHOD OF AGREEMENT AND DIFFERENCE 119 
II. Table of negative instances. 

3 s / 

^ii s u 

S s 

etc. etc. 

In the two sets of instances, the following con- 
ditions must be observed in order to render the 
method valid : — 

1. S + G, S'+ C, S" + C, S"' + C, etc., 

must be so varied that they reveal but one constant 
element, common to them all, as C. It may be that 
S will resemble S' in more marks than the one, 
namely C, and this may be true of any two or more 
instances ; however, taken all together, they must 
possess but the one common element, G. 

2. In the same way S t may resemble S n in more 
marks than merely the absence of C and so for any 
two or more instances in the series S t , S u , S IU , etc. 
However, the one characteristic common to them all 
must be the absence of C. 

3. If in the instances chosen an element is com- 
mon to all in addition to C, or in the second set its 
absence, then additional instances must be added to 
the tables both positive and negative in order to 
secure this all-important condition of elimination 
through suitable variation. 

4. Moreover, the two series, positive and negative, 
must have their settings similar. S„ S n , S ni , etc., 
must resemble S', S", S'", etc. ; otherwise the nega- 
tive instances would not be significant. They must 



120 INDUCTIVE LOGIC 

be chosen from the same sphere as the positive, that 
they may be similar. It is possible to multiply neg- 
ative instances ad infinitum, which, however, would 
furnish no ground for any inference, because they 
would be wholly irrelevant to the problem under 
investigation. 

5. If S, is so similar to S' as to be identical with 
it, and also s t pass over into s'; then we have the 
method of difference in its pure form : — 

S' + C s' + e 

S' s' 

Here the setting, instead of being similar in the two 
cases, is the same in each. 

The following is an experiment of Sir John Lub- 
bock's concerning the sense of smell in insects, which 
I have chosen as illustrating this method of induc- 
tive research. He took a large ant and tethered 
her on a board by a thread. When she was quite 
still, he brought a tuning-fork into close proximity 
to her antennae, but she was not disturbed in the 
least. He then approached the feather of a pen 
very quietly, so as almost to touch first one and 
then the other of the antennas, which, however, did 
not move. He then dipped the pen in the essence 
of musk and did the same ; the antenna was slowly 
retracted and drawn quite back. He then repeated 
the same with the other antenna, and with like 
result. Care was taken throughout not to touch 
the antennas. Lubbock then repeated the experi- 
ment with a number of different ants, and using 
various substances. The results in all cases were 



METHOD OF AGREEMENT AND DIFFERENCE 121 

the same, and the inference was naturally drawn 
that the antennae possessed the sense of smell. In 
these experiments, various substances were taken 
having nothing in common save the odor of musk 
that had been placed upon them. 

In some cases it is not possible to discover posi- 
tive instances in which the only common element 
is the suspected cause. In such cases the method 
is not conclusive in its results, although it may 
attain a high degree of probability, if all the com- 
mon elements save the suspected cause-element 
are known to be irrelevant, or can in any other way 
be proved to have no influence whatsoever upon the 
result. For instance, an illustration is often given 
of this method, which fails in the manner just de- 
scribed. A man is attempting to discover whether 
a particular article of food disagrees with him. 
He notices several occasions, a large number if 
you please, when he has eaten this particular kind 
of food, and has soon after experienced distress. 
These are the positive instances. This peculiar 
distress has never been experienced when he has 
abstained from the food in question. The inference 
is that this food has caused the distress. In the 
various instances, however, the sole element in 
common is not merely the taking or not taking the 
food. The person's whole bodily organism is com- 
mon to all the instances. Within it, unforeseen 
complications independent of this article of food 
might have caused the trouble. In such cases, 
number of instances must be resorted to in order to 
render the possibility of a coincidence impossible. 



122 INDUCTIVE LOGIC 

So also in such cases as the treatment of any given 
disease in a hospital. An experiment may be tried 
in the treatment, say, of typhoid fever. One ward 
may be subjected to a particular kind of treatment, 
and another ward not subjected to that treatment. 
If recovery is hastened in the one and retarded 
in the other case, an inference may be drawn as 
to efficacy of this treatment. In these instances 
again, while they are all different patients, still the 
nursing, surroundings, etc., are common to them 
all. It must be shown that these are present 
both in the negative and positive instances, and 
equally capable of accomplishing the effect if they 
had been real causes. They may therefore be 
eliminated in comparing the two sets of instances, 
because common both to the negative and positive 
cases. In this also resort must be had to the num- 
ber of instances in order to eliminate chance coin- 
cidences. The presence of common elements in 
excess of the common causal element may be rep- 
resented according to the symbolical notation of 
the joint method, by the introduction of another 
symbol x. Let x stand for that which is common 
to all instances in addition to the common element 
C. We then have : — 

I. Set of positive instances. 

S + C + x . . . . . . s + e 

S' + O + x s' + e 

S" + C + x s' +e 

S»i + C + x s'" + e 

etc. etc. 



METHOD OF AGREEMENT AND DIFFERENCE 123 

II. Set of negative instances. 

S t + x s t 

8„ + x s n 

"ill + x s lll 

etc. etc. 

We observe x in all instances both positive and 
negative. Being present when the effect occurs 
and when it does not, indifferently, we can at once 
infer that x is not the whole cause of e. However, 
it may have united with C in the first set of instances 
to produce the effect e, so that C without x, or some 
part or parts of x, could not alone produce the effect 
e. In all such cases the exact force of x must be 
estimated in some other way. If x is extremely 
complex, or subject to change from forces emanating 
from within itself, as in the case of organic phenom- 
ena, then it becomes extremely difficult to determine 
x ; and consequently the method of agreement and 
difference does not yield as exact results. As long 
as the force of x remains unknown, it becomes the 
source of possible disturbance, which may wholly 
vitiate the results attained. 

Mr. Darwin, in his experiments upon cross and 
self fertilization in the vegetable kingdom, placed 
a net about one hundred flower heads, thus protect- 
ing them from the bees and from any chance of 
fertilization by means of the pollen conveyed to 
them by the bees. He at the same time placed one 
hundred other flower heads of the same variety of 
plant where they would be exposed to the bees, and, 
as he observed, were repeatedly visited by them. 



124 INDUCTIVE LOGIC 

Here we have the two sets of instances, in one the 
flowers accessible to the bees, and in the other, not 
accessible. He obtained the following result. The 
protected flowers failed to yield a single seed. The 
others produced 68 grains weight of seed, which he 
estimated as numbering 2720 seeds. Cross-fertiliza- 
tion as the cause in this case is thus proved. The 
common element in all these instances, however, is 
not merely the presence in one case and the absence 
in the other of the bees ; there is also the element 
of the common plant structure running through all of 
the two hundred instances. This element is, how- 
ever, of such an unvarying nature in all the instances, 
and the number observed so many as to eliminate 
the possibility of any given plant structure possess- 
ing unobserved peculiarities sufficient to produce the 
result in question. It may therefore be considered 
as an inert element as regards the effects noticed in 
the one and absent in the other set of instances. 

Sir John Lubbock, in his researches concerning 
the different functions of the two kinds of eyes in 
insects, illustrates the joint method in its general 
features. The two kinds of eyes are the large com- 
pound eyes, situated one on each side of the head, 
and the ocelli, or small eyes, of which there are 
generally three, arranged in a triangle between the 
other two. He wished to determine the precise 
function of the small eyes, the ocelli; and he has 
gathered together the following facts. Plateau has 
shown that caterpillars, which possess ocelli, but no 
compound eyes, are very short-sighted, not seeing 
above one to two centimetres. He has also proved 



METHOD OF AGREEMENT AND DIFFERENCE 125 

by experiments that spiders, which have ocelli but 
no compound eyes, are very short-sighted ; they were 
easily deceived by artificial flies of most inartistic 
construction, and even hunting spiders could not 
see beyond ten centimetres (four inches). Lubbock 
experimented on this point with a female spider, 
which, after laying her eggs, had rolled them into a 
ball, and had enveloped the whole with a silken bag 
which she carried about with her. Having captured 
the female and having taken the bag of eggs from 
her, he placed it on a table about two inches in 
front of her. She evidently did not see it. He 
then pushed it gradually towards her, but she took 
no notice till it nearly touched her, when she eagerly 
seized it. He then took it away a second time, and 
put it in the middle of the table, which was two 
feet four inches by one foot four, and had nothing 
else on it. The spider wandered about for an hour 
and fifty minutes before she found it, apparently 
by accident. He then took it away again and put 
it down as before, when she wandered about for an 
hour without finding it. Like experiments were 
tried with other spiders and with the same results. 
Plateau also experimented with scorpions which 
had ocelli and no compound eyes. They appeared 
scarcely to see beyond their own pincers. More- 
over, the ocelli are especially developed in insects, 
such as ants, bees, and wasps, which live partly in 
the open light and partly in the dark recesses of 
nests. Again, the night-flying moths all possess 
ocelli. On the other hand, however, they are en- 
tirely absent in all butterflies, with, according 



126 INDUCTIVE LOGIC 

to Scudder, but one exception, namely, the genus 
Pamphila. Forel, moreover, varnished the com- 
pound eyes of various insects which had ocelli as 
well. The latter, however, he allowed to remain in 
their natural state. Inasmuch as their habits of 
flight required powers of vision in these insects 
extending to a considerable distance, it happened 
that when placed on the ground they made no at- 
tempt to rise; while, if thrown into the air, they 
flew first in one direction and then in another, 
striking against any object that came in their way, 
and being apparently quite unable to guide them- 
selves. They flew repeatedly against a wall, falling 
to the ground, and unable to alight against it, as 
they did so cleverly when they had their compound 
eyes to guide them. All these instances, taken 
together in their positive and negative aspects, led 
Sir John Lubbock to infer that the ocelli were use- 
ful in dark places and for near vision, while the 
compound eyes were for the light and more distant 
vision. 1 

Another illustration of this method may be found 
in Darwin's account of the extreme tameness of the 
birds in the Galapagos and Falkland islands. I 
qiiote some extracts from his narrative, in which it 
will be seen that Darwin's inferences follow from 
his comparison of the positive and negative instances 
before him. He says : " This tameness of dispo- 
sition is common to all the terrestrial species of 
these islands in the Galapagos Archipelago ; namely, 

1 Lubbock, On the Senses, Instinct, and Intelligence of Ani- 
mals, pp. 175 ff. 



METHOD OF AGREEMENT AND DIFFERENCE 127 

to the mocking-thrushes, the finches, wrens, tyrant 
flycatchers, the dove, and carrion-buzzard. All of 
them often approached sufficiently near to be killed 
with a switch, and sometimes, as I myself tried, 
with a cap or hat. A gun is here almost super- 
fluous; for, Avith the muzzle, I pushed a hawk off 
the branch of a tree. In Charles Island, which had 
been colonized about six years, I saw a boy sitting 
by a well with a switch in his hand, with which he 
killed the doves and finches as they came to drink. 
He had already procured a little heap of them for 
his dinner ; and he said that he had constantly been 
in the habit of waiting by this well for the same 
purpose. The Falkland Islands offer instances of 
birds with a similar disposition. The snipe, upland 
and lowland goose, thrush bunting, and even some 
true haAvks, are more or less tame. The black- 
necked swan is here wild, and it was impossible to 
kill it. It, however, is a bird of passage, which 
probably brought with it the wisdom learned in 
foreign countries. 

From these several facts, we may, I think, con- 
clude that the wildness of birds with regard to 
man, is a particular instinct directed against him 
and not dependent on any. general degree of caution 
arising from other sources of danger; secondly, 
that it is not acquired by individual birds in a 
short time, even when much persecuted, but that 
in the course of successive generations it becomes 
hereditary. With domesticated animals we are 
accustomed to see new mental habits or instincts 
acquired and rendered hereditary, but with animals 



128 INDUCTIVE LOGIC 

in a state of nature it must always be most difficult 
to discover instances of acquired hereditary knowl- 
edge. In regard to the wildness of birds towards 
man, there is no way of accounting for it except as 
an inherited habit : comparatively few young birds, 
in any one year, have been injured by man in 
England, yet almost all, even nestlings, are afraid 
of him ; many individuals, on the other hand, both 
at Galapagos and at the Falklands, have been pur- 
sued and injured by him, but yet have not learned 
a salutary dread of him." 1 

I have given this quotation somewhat at length 
in order to show the method of a great investigator 
in the realm of nature; and that it may be seen 
how naturally he falls into the method of compar- 
ing positive and negative sets of instances relative 
to the object of research. The animal and vege- 
table kingdoms are especially adapted to the appli- 
cation of this joint method, and therefore it is in 
biology that it is most frequently employed and 
where it has yielded the most fertile results. 

The advantage of the joint method over the sim- 
ple method of agreement is that it largely elimi- 
nates the possibility of there being any other cause 
of the given phenomenon than the one disclosed 
by the operation of this method. The method of 
agreement, as we have seen, often fails of a definite 
result owing to the plurality of causes. The joint 
method tends to indicate the one and only cause, 
and when the instances are rigorously selected ac- 
cording to the conditions of the canon, there is a 

1 Darwin, Voyage of a Naturalist, Vol. II. pp. 172 f. 



METHOD OF AGREEMENT AND DIFFERENCE 129 

high degree of probability that the sole cause is 
discovered. Mr. Mill at this point claims too much 
for the method in insisting that it gives a certainty 
regarding the sole cause, when the requirements 
are perfectly realized. It is impossible to realize 
the requirements perfectly. In selecting the nega- 
tive instances, we are never sure that we have 
compassed the entire sphere of significant negative 
instances. We may, however, attain results highly 
probable in this regard, though they may not reach 
an absolute certainty. Such a statement is more 
moderate in its expression, and practically it assures 
as satisfactory results. 



CHAPTER X 

The Method of Concomitant Variations 

The method of concomitant variations is a 
process of determining a causal relation when, as 
an element in an antecedent varies in intensity, 
greater or less, there is observed a corresponding 
or concomitant variation in the consequent. 

Canon of the Method of Concomitant Variations. — 
Whatever phenomenon varies in any manner, when- 
ever another phenomenon varies in some particular, 
is either a cause or an effect of that phenomenon, or 
is connected with it through some fact of causation. 

The latter clause of this canon provides for that 
circumstance in which the varying elements may 
both be concomitant effects of a common cause. 
When we are assured of the absence of any possi- 
ble common cause to which we can assign the two 
phenomena as effects, then they must be related 
between themselves as cause and effect. A simple 
illustration of this method is the rise of the mer- 
cury in the thermometer owing to the increase of 
heat; its fall, whenever there is decrease of heat. 
One varies as the other concomitantly, and we infer 
a causal relation that we at once proceed to gen- 
eralize without hesitation. 
130 



METHOD OF CONCOMITANT VARIATIONS 131 

The symbolical representation of this method is 
as follows : — 

S+ C s + e 

S + C ±dC s + e ±de 

etc. etc. 

Then C is the cause of e. 

I have used dC, and de to denote the increments 
or decrements of the cause and effect respectively. 
This method is used generally when the method of 
difference is impossible, owing to the fact that the 
supposed causal element cannot be made to vanish 
wholly. In all such cases a variation of the ele- 
ment is resorted to, and the corresponding result 
observed. Heat is relative and not absolute, as also 
the height of mercury in the tube. The relation 
is determined, therefore, by variations, greater and 
less. This method is also used to supplement the 
results of other methods by which a causal relation 
has been determined, but not in exact quantitative 
terms. It may be known that a certain phenome- 
non C is always the cause of a certain effect e, and 
the method of concomitant variations will then be 
of use in determining precisely how much of a vari- 
ation in C will cause a specified variation in e. A 
law finds scientific expression only when stated in 
terms of exact quantitative relation between varia- 
tions in antecedent and consequent. We may ex- 
press the law of universal attraction in a vague way 
that bodies always attract each other and the greater 
attraction when the bodies are nearer together, and 
the larger they are. But this statement needs to 



132 INDUCTIVE LOGIC 

be recast in terms exhibiting the precise quantita- 
tive variation. Bodies attract each other directly 
as the product of their masses, and inversely as the 
square of their distance. It is evident that the 
special function of this method of concomitant vari- 
ations consists in just this quantitative determina- 
tion. In one respect, therefore, it may be regarded 
as a substitute for the method of difference, and 
in another way as a supplement to the method of 
difference in leading to quantitatively determinate 
results. 

The quantitative variation between antecedent 
and consequent may be either direct or inverse vari- 
ation. The former is when one increases as the 
other increases, or when one decreases as the other 
decreases. The inverse is when one decreases as the 
other increases, or vice versa. This may be expressed 
symbolically 

S+C±dC . . . . s+eTde 

We have, for instance, Boyle's law as regards the 
variation of volume of gases according to the press- 
ure ; that is, when we double the pressure, we halve 
the volume. This may be proved experimentally. 
The method also was used by Kicardo to prove his 
law that the rate of profits varies in inverse ratio to 
the rate of wages. We have also the tendency ob- 
served in respect to increase of crimes, when there 
is decrease of opportunities for labor. 

The expression of a law in terms of the quantita- 
tive relation between antecedent and consequent 
may be facilitated by a graphic representation of the 



METHOD OF CONCOMITANT VARIATIONS 133 

same, through corresponding abscissae and ordinates. 
The varying antecedents, for instance, may be laid 
off on the axis of X, and each several consequent 
represented by the corresponding ordinates. The 
resulting curve thus obtained will represent the law 
of their mutual relation. If the equation of the 
curve can be determined, it will represent the math- 
ematically exact expression of the law in question. 
If this is not possible, it may prove at least sug- 
gestive of the law which otherwise might have 
remained concealed. This graphical method is 
especially useful in dealing with physical phenom- 
ena. " If the abscissae represent intervals of time, 
and the ordinates corresponding height of the ba- 
rometer, we may construct curves which show at a 
glance the dependence of barometric pressure upon 
the time of day. Such curves may be accurately 
drawn by photographic processes on a sheet of sen- 
sitive paper placed behind the mercurial column, 
and made to move past it with a uniform horizontal 
velocity by clockwork. A similar process is applied 
to the temperature and electricity of the atmosphere, 
and to the components of terrestrial magnetism." 1 

This method, moreover, has the advantage of the 
psychological impression which it makes. The 
mind is more susceptible to the perception of varia- 
tion in forces where the change is apparent to the 
senses, than to the perception of a constant force, 
whose constant character thereby conceals its nat- 
ure and function from the senses. Synchronous 

1 Thomson and Tait, Elements of Natural Philosophy, Vol. 
I. p. 119. 



134 INDUCTIVE LOGIC 

changes attract the attention, and admit of ready 
comparison, as we follow out the variations from 
point to point. We may ring a bell in a vacuum, 
and detect no sound whatsoever, and then allow the 
air to enter gradually. We notice that as the air 
enters more and more freely, the sound grows 
louder and louder. The relation of cause and effect 
is thus demonstrated to the senses in the most vivid 
manner possible. The variations are exhibited side 
by side, and thus, presented together in their con- 
comitant relation, produce the deeper impression. 

This method is of special advantage in all experi- 
ments where the intensity of the forces can be 
varied at will and the consequent effects exhibited 
in some palpable manner. The determination of 
the heat rays in the solar spectrum is accomplished 
by this method. The spectrum may be received 
upon a plate pierced with a narrow slit, through 
which the rays can act upon a thermo-electric pile, 
which will indicate by deflections of a needle the 
varying intensity of the heat in the several rays of 
the spectrum. Now, move the slit through the 
whole extent of the spectrum, beginning with the 
violet portion. While in the violet, the indigo, 
the blue, and even the green, the needle of the ther- 
moscopic apparatus will be deflected but slightly, 
it will indicate an amount of heat increasing as 
the slit crosses the yellow, next the orange, then 
the red ; and then bej^ond the red, and entering the 
dark portion of the spectrum, we find the greatest 
deflection of all. The maximum of heat is there- 
fore in a region beyond the observation of the 



METHOD OF CONCOMITANT VARIATIONS 135 

senses when unaided by experimental device ; and 
yet revealed conclusively by this method. 1 

Professor Tyndall performed a very interesting 
experiment to prove that the cloud of darkness sur- 
rounding flames of great heat was due to the fact 
that the heat consumed the floating motes in the 
air which serve to scatter the light which is visible 
only when thus diffused. The phenomenon which 
he endeavored to explain was somewhat as follows : 
Beneath a beam of electric light, a red-hot poker 
was placed, and from it black wreaths as of smoke 
were seen to ascend. A large hydrogen flame being 
employed, it produced whirling masses of darkness 
far more copiously than the poker. Of this Pro- 
fessor Tyndall remarked : " Smoke was out of the 
question ; what then was the blackness ? It was 
simply that of stellar space ; that is to say, blackness 
resulting from the absence from the track of the 
beam of all matter competent to scatter its light. 
When the flame was placed below the beam, the float- 
ing matter was destroyed in situ; and the air freed 
from this matter rose into the beam, jostled aside 
the illuminated particles, and substituted for their 
light the darkness due to its own perfect transpar- 
ency. Nothing could more forcibly illustrate the 
invisibility of the agent which renders all things 
visible. The beam crossed, unseen, the black chasm 
formed by the transparent air, while at both sides 
of the gap the thick-strewn particles shone out like 
a luminous solid under the powerful illumination." 2 

1 Saigey, The Unity of Natural Phenomena, p. 61. 

2 Tyndall, Fragments of Science, p. 280. 



136 INDUCTIVE LOGIC 

Such being the phenomenon and Professor Tyndall's 
explanation, it will be seen that he proceeded accord- 
ing to the method of concomitant variations in the 
following experiment of many which he performed 
to substantiate this theory : — 

A platinum tube, with its plug of platinum 
gauze, was connected with an experimental tube, 
through which a powerful beam could be sent 
from an electric lamp placed at its end. The 
platinum tube was heated till it glowed feebly 
but distinctly in the dark. The experimental tube 
was then exhausted, and filled with air that had 
passed through the red-hot tube. A considerable 
amount of floating matter which had escaped com- 
bustion was revealed by the electric beam. 

Then the tube was raised to a brighter redness 
and the air permitted to pass slowly through it. 
Though diminished in quantity, a certain amount 
of floating matter passed into the exhausted ex- 
perimental tube. 

The platinum tube was rendered still hotter; a 
barely perceptible trace of the floating matter now 
passed through it. The experiment was repeated, 
with the difference that the air was sent more 
slowly through the red-hot tube. The floating 
matter was totally destroyed. 

The platinum tube was now lowered until it 
bordered upon a visible red heat. The air, sent 
through it still more slowly than in the last ex- 
periment, carried with it a cloud of floating mat- 
ter. Professor Tyndall's commentary upon this 
experiment is as follows : " If, then, the sus- 



METHOD OF CONCOMITANT VARIATIONS 137 

penclecl matter is destroyed by a bright red heat, 
much more is it destroyed by a flame, whose tem- 
perature is vastly higher than any employed in 
this experiment. So that the blackness intro- 
duced into a luminous beam where a flame is 
placed beneath it is due, as stated, to the destruc- 
tion of the suspended matter." ' 

Professor Tyndall also supplemented this experi- 
ment by one which was according to the joint 
method of agreement and difference. He prepared 
oxygen so as to exclude all floating particles, and 
found that when blown into the beam, darkness 
was produced ; also that hydrogen, nitrogen, car- 
bonic acid, and coal-gas, when prepared in a similar 
way, each produce darkness when poured or blown 
into the beam. These instances, combined with 
various positive instances of illumination of mote- 
strewn currents of air, illustrate the method of 
agreement and difference. 

An additional experiment, according to the method 
of difference, was as follows : Professor Tyndall 
placed an ordinary glass shade in the air with its 
mouth downward. This permitted the track of the 
beam to be seen crossing it. Letting coal-gas, or 
hydrogen, enter the shade by a tube reaching to 
its top, the gas gradually filled the shade from the 
top downward. As soon as it occupied the space 
crossed by the beam, the luminous track was in- 
stantly abolished. Lifting the shade so as to bring 
the common boundary of gas and air above the 
beam, the track flashed forth. After the shade was 

1 Tyndall, Fragments of Science, pp. 283, 284. 



138 INDUCTIVE LOGIC 

full, he inverted it; thereupon the gas passed up- 
ward like a black smoke among the illuminated 
particles. 1 

The method of concomitant variations is not 
only capable of illustration by laboratory methods 
and devices ; it finds abundant illustration as well 
in the realm of nature, where observation alone 
becomes the instrument of investigation and where 
experiment is impossible or impracticable. Lyell, 
in his Principles of Geology, gives a very interest- 
ing account of the alternate elevation and subsi- 
dence of the temple of Jupiter Serapis, at Pozzuoli, 
on the Bay of Naples. 2 It is situated in proximity 
to several volcanoes, Vesuvius, however, being at 
some distance. It has been observed that there is 
a certain connection between each era of upheaval, 
and a local development of volcanic heat; and on 
the other hand, between each era of depression, and 
the local quiescent condition of volcanic phenomena. 
Before the Christian era, when Ischia was in a state 
of eruption, and Avernus and other points in the 
Phlegrsean fields were celebrated for their volcanic 
character, it was observed that at that time the 
ground on which the temple stood was several feet 
above water. Vesuvius was then regarded as a spent 
volcano. After the Christian era, Vesuvius became 
active and then scarcely a single eruption occurred 
in Ischia or around the Bay of Baise. It was ob- 
served that at that time the temple was sinking. 
Vesuvius then became quiet for five centuries pre- 

1 Tyndall, Fragments of Science, pp. 284,285. 

2 Chapter XXX. 



METHOD OF CONCOMITANT VARIATIONS 139 

ceding the eruption of 1631, and during that period 
the Solfatara was in eruption in 1198, Ischia in 1302, 
and Monte Nuovo was formed in 1538. Then the 
foundations of the temple were observed to be ris- 
ing again. Vesuvius became active after that, and 
has continued so ever since, and during this time 
the temple has been subsiding. The inference is 
that as the subterranean heat increases, and lava 
forming without obtaining an easy vent like that 
afforded by Vesuvius, the surface is elevated, but 
when the rocks below are cooling and contracting, 
the pent-up fire being withdrawn in the eruption of 
the great Vesuvius, then there is a corresponding 
subsidence. 

The observation of concomitant variations is 
furthermore illustrated in Darwin's researches con- 
cerning the formation of coral reefs, as regards the 
question which some naturalists have raised as to 
which part of the coral reef is most favorable to the 
growth of coral. 1 He adduces the following facts, 
most of which are the direct result of his observa- 
tions : " The great mounds of living Porites and of 
Millepora round Keeling atoll occur exclusively 
on the extreme verge of the reef, which is washed 
by a constant succession of breakers. At the Mar- 
shall Islands the larger kinds of coral which form 
rocks measuring several fathoms in thickness pre- 
fer the most violent surf. The outer margin of the 
Maldiva atolls consists of living corals, and here 
the surf is so tremendous that even large ships 
have been thrown, by a single heave of the sea, 
1 Darwin, Coral Reef s, pp. 87 f. 



140 INDUCTIVE LOGIC 

high and dry on the reef, all on board thus escap- 
ing with their lives. In the Red Sea the strongest 
corals live on the outer reefs and appear to love the 
surf. From these facts it is certain that the strong- 
est and most massive corals flourish where most 
exposed. The less perfect state of the reef of most 
atolls on the leeward and less exposed side, com- 
pared with its state to the windward, and the anal- 
ogous case of the greater number of breaches on the 
rear sides of those atolls in the Maldiva Archipelago, 
which afford some protection to each other, are obvi- 
ously explained by this circumstance." There seems 
to be here a combination of the method of agree- 
ment with that of concomitant variations. And 
such a combination may be employed to advantage 
in cases where the phenomena under investigation 
show forces under varying degrees of intensity; 
the, causal relation is more apparent, and the pos- 
sibility of fortuitous coincidence is largely elimi- 
nated if a number of instances can be collected 
in which the forces manifest themselves in vary- 
ing degrees. Accumulation of instances, showing 
concomitant variations in the forces observed, cor- 
responds to the actual variations which in an experi- 
ment are effected by the investigator himself. In 
such observed instances, however, we cannot always 
have before us the variations expressed continuously. 
There are evident gaps that must be interpolated 
mentally. In the experiment, however, of whatever 
nature, the degrees of intensity can be exhibited 
continuously, one degree merging into another 
through inappreciable increments. There is thus 



METHOD OF CONCOMITANT VARIATIONS 141 

a gradation which has no gaps to be filled, and the 
psychological impression is thereby heightened. 

By the method of concomitant variations it is 
possible also to represent to the mind the magni- 
tude of an unknown force, or unobservable force 
by comparison with the intensity of a known force, 
which lies within the sphere of observation. For 
instance, Mr. Darwin gives an interesting account 
in his narrative of the finding near the shores of 
the Plata a group of vitrified silicious tubes which 
had been formed by lightning entering loose sand. 
The internal surface of such tubes is completely vit- 
rified, glossy, and smooth, and the tubes themselves 
are generally compressed, and have deep longitu- 
dinal furrows so as closely to resemble a shrivelled 
vegetable stalk, or the bark of an elm or cork tree. 
Their circumference is about two inches, but in 
some fragments which are cylindrical and without 
any furrows, it is as much as four inches. Judging 
from the uncompressed fragments, the measure or 
bore of the lightning proved to be about one inch 
and a quarter. In contrast with the force of light- 
ning as thus revealed in its effects, Mr. Darwin cites 
some experiments performed in Paris by an artifi- 
cial force of great magnitude indeed and yet with 
results that seem insignificantly small in compari- 
son. He says : " At Paris, M. Hatchette and M. 
Beudant succeeded in making tubes in most respects 
similar to these fulgurites by passing very strong 
shocks of galvanism through finely powdered glass : 
they failed, however, both with powdered felspar 
and quartz. One tube, formed with pounded glass, 



142 INDUCTIVE LOGIC 

was very near an inch long, namely, .982, and had 
an internal diameter of .019 of an inch. When we 
hear that the strongest battery in Paris was used, 
and that its power on a substance of such easy fusi- 
bility as glass was to form tubes so diminutive, we 
must feel greatly astonished at the force of a shock 
of lightning, which, striking the sand in several 
places, has formed cylinders in one instance at least 
thirty feet long, and having an internal bore, where 
not compressed, of full an inch and a half ; and 
this in a material so extraordinarily refractory as 
quartz ! " * 

The method of concomitant variations may be 
used in regard to phenomena whose nature is such 
as seemingly to indicate a constant law of variation, 
and yet inferences based thereupon lead to false 
results. It is, therefore, well to note some of these 
instances by way of general precaution in applying 
this method. 

1. It does not necessarily follow that having 
observed two forces varying in a constant ratio 
through several concomitant modifications, the 
same ratio will be preserved indefinitely through 
all subsequent changes. Water contracts as it is 
cooling. Suppose we begin to note this continued 
contracting of water from 100° F. to 90°; we natu- 
rally expect to find it continuing through 90° to 80°. 
And as we observe, we find our expectations con- 
firmed. And so on through to 40°, we find that 
water continues to contract. It is, therefore, most 
natural for us to expect to find water contracting 

1 Darwin, Voyage of a Naturalist, Vol. I. pp. 76 f . 



METHOD OF CONCOMITANT VARIATIONS 143 

at 39°. But just at this point in the series, there is 
a break in the continuity of variation ; at 39° water 
begins to expand and so continues until it passes into 
the solid form at the freezing-point. The same also 
is illustrated in Weber's law, already mentioned, 
which expresses the quantitative relation between 
the stimulus and the corresponding sensation. The 
law is that the force of the stimulus must increase 
geometrically, in order that the intensity of the 
sensation should increase arithmetically. This law, 
however, breaks down towards the upper or lower 
limits, with a stimulus of slight degree of intensity 
and with one of extreme intensity. We find also 
an increase of temperature as we proceed towards 
the centre of the earth of about one degree to 
every fifty-three feet of descent. This by no means 
warrants us in inferring that this ratio continues 
constant to the very centre itself. In certain 
phenomena, moreover, there are natural limits, as 
in sound, for example, where the pitch rises as the 
number of vibrations increases. At a certain point, 
varying according to different individuals, increase 
of vibrations gives no resulting sound whatsoever; 
and so there is a lower limit, vibrations may 
decrease to a point beyond which no sound is 
heard. 

An illustration of this fallacy, though not strictly 
of the method of concomitant variations, is given 
by Jevons. He takes the following series of prime 
numbers: 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 
etc. It will be seen that they all agree in being 
values of the general expression x 2 + x + 41, 



144 INDUCTIVE LOGIC 

where we put for x the successive values of 0, 1, 
2, 3, 4, etc. For instance, let x = i\\x 2 -\-x + 
41, we get 41 ; let x = 1 in the same, we get 43 ; 
when x = 2, we get 47 ; and so on. It seems as 
though we could keep this up indefinitely, produc- 
ing an increasing series, always of prime numbers. 
It is found, however, that if we take x = 40, in 
the formula x 2 + x-\- 41, we shall have 40x40 
+ 40 + 41, which equals 1681, and this number is 
the square of 41 and therefore not a prime number. 
At this point the law breaks down. 1 

In the sphere of political economy also we might 
be led into an easy yet false inference. Suppose 
a certain farm yield 500 bushels of corn with a 
given amount of expenditure and labor. We might 
think that if we doubled the expenditure and 
labor, we will also be able to double the results, 
and obtain a yield of 1000 bushels as over against 
the 500 of the previous year. Here, however, what 
is known as the law of decreasing returns obtains ; 
to double the product it may be necessary to triple 
or quadruple the labor and expense. " Thus in the 
production of any plot of land there is a point of 
equilibrium, which marks an impassable limit, not 
of course a limit which could not be passed if it 
were wished, but one that no one wishes to pass, 
because there is nothing to be gained by so doing." 2 

To know that such false inferences are at least 
possible in the application of this method of con- 
comitant variations to the unknown regions beyond 

1 Jevons, Principles of Science, p. 230. 

2 Gide, Political Economy, p. 325. 



METHOD OF CONCOMITANT VARIATIONS 145 

our experience, may serve at least to keep us on 
guard under similar circumstances. 

2. There are certain phenomena, moreover, in 
which an increased intensity of the force in ques- 
tion may give rise to incidental effects which tend 
to neutralize the chief effect to be attained. For 
instance, an overdose of arsenic causes violent 
contractions of the stomach so that its contents 
are immediately ejected, and thus the system is 
relieved of the noxious substance. 

3. Two elements in a given phenomenon may 
vary together constantly and yet they may not be 
related at all as cause and effect, but appear as coin- 
cidental effects of one and the same cause. It has 
been observed that the occurrence of the Aurora 
Borealis has been accompanied by pronounced mag- 
netic disturbances. It, however, cannot be inferred 
that the former has been the cause of the latter ; 
they are probably the varied effects of some widely 
operating magnetic force. 

The precaution above mentioned has already been 
referred to as provided for in the canon of this 
method which states that the observed concomitant 
variation may indicate not always a direct causal 
element between the two varying elements, but 
that they are at least connected with the phe- 
nomenon under investigation through some fact of 
causation. 






CHAPTER XI 

The Method of Residues 

The method of residues consists in the analysis 
of a given phenomenon based iipon previous induc- 
tions, through which it has been determined that 
certain elements in the antecedent have caused 
certain elements in the consequent ; the inference 
is then drawn, that the remaining elements of the 
antecedent are necessarily the cause of the remain- 
der of the consequent. It is a method of elimina- 
tion of the known relations so as to simplify the 
complex character of the phenomenon and disclose 
the relations that are unknown in the light of a 
causal connection which we are constrained to be- 
lieve must obtain. 

The Canon of the Method of Residues. — Subduct 
from any phenomenon such part as is known by 
previous inductions to be the effect of certain ante- 
cedents, and the residue of the phenomenon is the 
effect of the remaining antecedents. 

The symbolical representation is as follows : — 

Given S+C s-\-e 

If it is known that there exists the causal relation 

S . s, 

146 



THE METHOD OF RESIDUES 147 

we may then infer that C is the cause of e. In 
this C may be simple or complex ; if it is simple, 
the causal relation established is expressed in its 
simplest terms and is therefore a determinate result. 
If, however, the residue C is complex, it must be 
reduced by experimental analyis to its simplest 
elements, and their relation to the elements into 
which e can be analyzed further determined. 

The most striking illustration of this method, and 
one of the most brilliant achievements of science 
as well, is the discovery of the planet Neptune by 
Adams and Le Verrier, working on the problem in- 
dependently and reaching the same result. These 
astronomers had observed certain perturbations in 
the planet Uranus. It did not keep in its proper 
orbit as determined by their mathematical calcula- 
tions based upon the presence of the known stellar 
bodies. It behaved as though beyond its orbit was 
an outer planet, whose presence alone could account 
for the observed perturbations. Adams and Le 
Verrier then proceeded to calculate the exact posi- 
tion of such a disturbing body as determined by 
the nature and magnitude of the perturbations of 
Uranus. The telescope was then pointed to the 
exact point in the heavens, as thus indicated, and 
the planet Neptune was revealed to the eye accord- 
ing to the determination of far-reaching prophecy, 
which confidently asserted that it must be there. 

The method of residues is really a deductive 
method based upon the law of sufficient reason ; so 
many elements on the one hand producing so many 
elements on the other ; if, then, a part of the former 



148 INDUCTIVE LOGIC 

is to be checked off as cause of a part of the latter, 
then the remainder on one hand must be the cause 
of the remainder on the other. This is pure de- 
duction. For we ask, Why are we constrained to 
account for the remainder on one side by the re- 
mainder on the other ? The only possible answer 
is that it must be accounted for within the system 
to which it is referred ; and but one part therein is 
left which can possibly account for it, because all 
the others are specifically determined in the known 
effects which they have produced. This method, 
however, has a proper place among the inductive 
methods, inasmuch as it is based on previous induc- 
tions, and leads to investigations that can be prose- 
cuted only by the various inductive processes of 
experiment. 

When the residue of the antecedent is a simple 
element, and no other possible causal element can 
lie concealed from our observation, then the infer- 
ence is simple and conclusive. A difficulty, how- 
ever, may present itself, owing to the fact that the 
residual element is apt to be complex and leave the 
phenomenon still indeterminate, or there may be a 
lurking element unnoticed by us which is the real 
cause in question. The function of this method is, 
therefore, largely suggestive. It says the effect is 
not wholly accounted for by the known causal ele- 
ments ; there is a residue unaccounted for, and its 
cause is to be sought in the residue of the antece- 
dent, and if it is thought that the whole of the 
antecedent is comprehended, the question is started, 
May there not be unobserved circumstances of the 



THE METHOD OF RESIDUES 149 

antecedent that further experiment will be calcu- 
lated to reveal? In many cases, therefore, this 
method must be supplemented by some other ex- 
perimental method in order to secure more precise 
determination, generally the method of difference. 
It often happens in investigations in chemistry, 
astronomy, and physics, that the actual phenomena 
vary in greater or less degree from their expected 
behavior according to established theory. This 
must lead either to a reconstruction of theory, or 
to a search for some unobserved force sufficient to 
account for the discrepancy. Herschel was the 
first to point out the significance of such discrep- 
ancies in scientific research, and he called them 
residual phenomena. 

An illustration of such a situation and the solu- 
tion of the problem thus presented is that of Sir 
Humphry Davy's experiments upon the decomposi- 
tion of water by galvanism. "He found that 
besides the two components of water, oxygen and 
hydrogen, an acid and alkali were developed at the 
two opposite poles of the machine. As the theory 
of the analysis of water did not give reason to ex- 
pect these products, they were a residual phenome- 
non, the cause of which was still to be found. The 
insight of Davy conjectured that there might be 
some hidden cause of this portion of the effect ; the 
glass containing the water might suffer partial 
decomposition, or some foreign matter might be 
mingled with the water, and the acid and alkali be 
disengaged from it, so that the water would have 
no share in their production. Assuming this, he 



150 INDUCTIVE LOGIC 

proceeded, to try whether the total removal of the 
cause would destroy the effect produced. By the sub- 
stitution of gold vessels for the glass, without any 
change in the effect, he at once determined that the 
glass was not the cause. Employing distilled water, 
he found a marked diminution of the quantity of acid 
and alkali evolved; yet there was enough to show 
that the cause, whatever it was, was still in opera- 
tion. The impurity of the water, then, was not the 
sole, but a concurrent cause. He now conceived 
that the perspiration from the hands touching the 
instruments might affect the case, as it would con- 
tain common salt, and an acid and alkali would 
result from its decomposition under the agency of 
electricity. By carefully avoiding such contact, he 
reduced the quantity of the products still further, 
until no more than slight traces of them were per- 
ceptible. What remained of the effect might be 
traceable to impurities of the atmosphere decom- 
posed by contact with the electrical apparatus. 
An experiment determined this ; the machine was 
placed under an exhausted receiver, and when thus 
secured from atmospheric influence, it no longer 
evolved the acid and alkali." 1 

By means of the suggestions incident upon this 
method, Bunsen, in 1860, discovered two new alka- 
line metals, caesium and rubidium. He was ex- 
amining alkalies produced by the evaporation of 
mineral water from Durkheim. The flame of these 
salts was examined by the spectroscope. Bunsen 
discovered several bright lines which he had never 

1 Gore, The Art of Scientific Discovery, pp. 432, 433. 



THE METHOD OF RESIDUES 151 

noticed before, and which he knew could not be 
produced by potash or soda, whose corresponding 
lines were in close proximity. He then subjected 
the mixture to a searching analysis and succeeded 
in obtaining two new alkaline substances. When 
he had separated them, he then tested them by the 
method of difference, by which he found that they 
were capable of producing the lines at first noticed ; 
but when withdrawn, the lines instantaneously dis- 
appeared. 

Thomson and Tait, in their Elements of Natural 
Philosophy, have the following reference and 
illustration of this method. " When, in an ex- 
periment, all known causes being allowed for, 
there remain unexplained effects (excessively 
slight it may be), these must be carefully inves- 
tigated, and every conceivable variation of ar- 
rangement of apparatus, etc., tried ; until, if 
possible, we manage so to exaggerate the residual 
phenomenon as to be able to detect its cause. It 
is here, perhaps, that in the present state of 
science we may most reasonably look for exten- 
sions of our knowledge ; at all events, we are 
warranted by the recent history of natural phi- 
losophy in so doing. Thus, to take only a very 
few instances, and to say nothing of the discovery 
of electricity and magnetism by the ancients, the 
peculiar smell observed in a room in which an 
electrical machine is kept in action was long 
ago observed, but called the ' smell of electricity,' 
and thus left unexplained. The sagacity of Schon- 
bein led to the discovery that this is due to the 



152- INDUCTIVE LOGIC 

formation of ozone, a most extraordinary body, 
of enormous chemical energies ; whose nature is 
still uncertain, though the attention of chemists 
has for years been directed to it." x 

Another illustration of this method is seen in 
the comparison of the observed and calculated 
positions of Encke's comet. It was found that 
the comet returned a little sooner than it should 
have done, the period regularly decreasing from 
1212.79 days, between 1786 and 1789, to 1210.44 
between 1855 and 1858. The inference has been 
that there is a resisting medium, as the ether, 
filling the space through which the comet passes. 
What the resisting medium is, and its nature, is 
of course a matter of conjecture as far as re- 
vealed by this method alone. The method merely 
indicates some resisting medium to account for 
the observed discrepancy. 2 

Herschel has observed that all great astronom- 
ical discoveries have been disclosed in the form 
of residual differences. The practice was intro- 
duced by Halley, when astronomer royal, of 
comparing systematically the positions of the 
heavenly bodies as actually observed with what 
might have been expected theoretically. His re- 
ductions of the lunar observations gave a series 
of residual errors, extending from 1722 to 1739. 
These were carefully tabulated, and formed the 
basis for certain modifications of the lunar theory. 3 

1 Thomson and Tait, Elements of Natural Philosophy, Vol. I. 
pp. 113 f . 

2 Jevons, Principles of Science, p. 570. 3 Ibid. p. 572. 



THE METHOD OF RESIDUES 153 

A discrepancy was observed by Newton between 
the theoretical and actual velocity of sound ; the 
former being 968 feet per second, and the latter 
1142. Newton's experiments and calculation were 
both inaccurate; nevertheless, a real discrepancy 
has been proved to exist, the theoretical being 
916 and the real velocity 1090 feet per second. 
In 1816 La Place showed this difference to be 
due to the heat evolved by the sudden compres- 
sion of the air during the propagation of the 
sound wave, the heat having the effect of in- 
creasing the elasticity of the air, and therefore 
appreciably accelerating the sound impulse. 

It sometimes happens that in repeating an ex- 
periment, we are confronted with evidently different 
results. Then, we may be sure, the experiment has 
been carelessly or inaccurately performed ; or else 
there are some disturbing causes not observed by 
us. On the other hand, however, if there is no 
likelihood of coincidence on repeated trials, yet, 
nevertheless, a marked agreement is noticed in the 
results of various trials, the mind should be at 
once alert to discover the hidden cause of such 
agreement, and possibly may be led to new truths 
of great importance. The following illustration is 
given by Thomson and Tait : " With a very good 
achromatic telescope a star appears to have a sensi- 
ble disc. But, as it is observed that the discs of all 
stars appear to be of equal angular diameter, we of 
course suspect some common error. Limiting the 
aperture of the object-glass increases the appear- 
ance in question, which, on full investigation, is 



154 INDUCTIVE LOGIC 

found to have nothing to do with discs at all. It 
is, in fact, a phenomenon due to diffraction of 
light." 1 

It was said of Darwin that in his researches the 
residual phenomena were always the special objects 
of his attention. His son, Francis Darwin, says of 
him: "There was one quality of mind which seemed 
to be of special and extreme advantage in leading 
him to make discoveries. It was the power of 
never letting exceptions pass unnoticed. Every- 
body notices a fact as an exception when it is strik- 
ing or frequent, but he had a special instinct for 
arresting an exception. A point apparently slight 
and unconnected with his present work is passed 
over by many a man almost unconsciously, with 
some half-considered explanation, which is in fact 
no explanation. It was just these things that he 
seized upon to make a start from. In a certain 
sense there is nothing special in this procedure, 
many discoveries being made by means of it. I 
only mention it, because, as I watched him at his 
work, the value of this power to an experimenter 
was so strongly impressed upon me." 2 This is 
striking testimony as to the practical worth of this 
method as an instrument of research. 

This method has also been applied to the more 
practical usage of examining the refuse of manu- 
factured and other products in order to discover 

1 Thomson and Tait, Elements of Natural Philosophy, Vol. I. 
p. 114. 

2 F. Darwin, Life and Letters of Charles Darwin, Vol. I. 
p. 125. 



THE METHOD OF RESIDUES 155 

some concealed utility. The analysis of coal-tar 
refuse has led to the discovery of many valuable 
substances that have proved of use in the arts, and 
in medicine as well. Glauber, the eminent chemist, 
and a discoverer of several chemical compounds, 
said he made it a rule to examine what every other 
chemist threw away. 



CHAPTER XII 

Verification and Prediction 

The Inducto-deductive Method. — We have seen 
that the inductive methods are efficient in revealing 
the cause of a given phenomenon under investiga- 
tion; and yet they do not warrant us in general- 
izing the special instance so as to formulate a 
universal law. There is always the possibility 
that while the special case which we experiment 
upon may give us indications of an existing causal 
relation, still a wider experience might disprove, or 
else modify materially our conclusions. The well- 
recognized fact of the plurality of causes and the 
intermixture of effect further embarrasses us in 
the attempt to rise to a law having universal sig- 
nificance and validity. The results of the induc- 
tive methods, therefore, need to be supplemented 
by some corroborative observations or experiments 
that will conclusively verify the results as obtained. 
This supplementary method is one which combines 
deduction with induction. Mr. Mill calls it the 
Deductive Method. It is, however, more ade- 
quately designated by the name, the Inducto-de- 
ductive Method. It consists of three stages : — 

1. Obtaining, by the inductive methods already 
156 



VERIFICATION AND PREDICTION 157 

described, the evidence of some existing causal 
connection, tentatively expressed in the form of a 
universal law. 

2. Regarding this universal law as the basis for 
subsequent deductions, by which we gain a knowl- 
edge of the nature of unknown phenomena, as 
necessitated by the conditions of this law. 

3. Verifying the results thus obtained by their 
correspondence with the phenomena as actually 
observed. Where this correspondence is wanting, 
then either the law was not correctly expressed, or 
there must have been some error in our deduction 
based upon it. When we are assured that the lat- 
ter is not the case, then a discrepancy between the 
theoretically deduced result and the actual facts as 
observed, always discredits our original induction. 
This method of verification serves as a check upon 
hasty generalization, on the one hand; and on the 
other, it serves to extend our knowledge into un- 
known regions, and is valuable as a means of scien- 
tific prediction. In the development of scientific 
knowledge, it has been a potent factor in enlarging 
the bounds of knowledge beyond the sphere of im- 
mediate observation. 

This combined process of reasoning is the one 
commonly employed by us all. Induction and de- 
duction are not separate processes, but, as before 
remarked, they are complementary factors in the 
one actual process of reasoning. We are con- 
tinually using our inductions as a deductive basis, 
inferring how things should be before they are 
really seen; and, when seen, at once instinctively 



158 INDUCTIVE LOGIC 

comparing prior inference with, present fact, we 
are either confirmed in our reasoning process, or 
compelled to discard our previous inference as 
false or inadequate as the case may be. Our 
world, the world of knowledge, is built up of the 
seen, and the unseen as well, because necessitated 
by inferences growing out of the seen which we are 
constrained to make ; the unseen which we thus 
are continually building into the seen and regard- 
ing it as though the known, we are, however, 
from time to time compelled to alter, and here and 
there tear down what we have too rashly builded 
up, as the structure is put to the test of verifying 
fact. 

This method of verification was used to decide 
between inferences drawn by Newton and Huy- 
ghens respectively, regarding the nature of light. 
Newton's observations led him to infer that light 
consisted of particles of matter shot out from the 
sun. Huyghens insisted that light consisted in the 
propagation of some kind of disturbance in the man- 
ner of a wave-motion. Newton's theory being taken 
as established, it would necessitate that light on 
entering a denser body of water, being refracted 
more nearly in a direction perpendicular to the 
surface, should, accordingly, move faster in the 
denser body than in the rarer one outside. On 
the other hand, according to Huyghens' theory, the 
opposite effect should take place, — light being re- 
fracted towards the vertical at the horizontal sur- 
face of a dense body such as water, its velocity in 
the dense body should be less than its velocity in 



VERIFICATION AND PREDICTION 159 

the rare body. The experiments separately ma.de 
by Fizeau and Foucault, both gave the result that in 
water light moves slower than in air, and therefore 
the theory of Huyghens, which was in accord with 
such a fact, was verified, and the theory of Newton, 
which was radically out of harmony with such a 
fact, was discredited. 1 

We cannot theorize concerning nature to any con- 
siderable extent without resorting to nature again 
to correct aberrations of reason, and the false 
fancies of the imagination. Theory, if correctly 
formulated, will always lead to a representation 
of facts as they are ; just as facts as they are, if 
rightly interpreted, will always lead to correct 
theory. 

The following are illustrations of the value of 
this method in predicting results before unknown. 

"Halley had the glory of having first detected a 
periodic comet in the case of that which has since 
borne his name. In 1705, Halley explained how 
the parabolic orbit of a planet may be determined 
from three observations; and joining example to 
precept, himself calculated the positions and orbits 
of twenty-four comets. He found, as the reward 
of his industry, that the comets of 1607 and 1531 
had the same orbit as that of 1682. And here the 
intervals are nearly the same, namely, about seventy- 
five years. Are these three comets then identical ? 
In looking back into the history of such appear- 
ances, he found comets recorded in 1456, in 1380, 
and 1305; the intervals are still the same, — sev- 

1 Tait, Recent Advances in Physical Science, pp. 65, 66. 



160 INDUCTIVE LOGIC 

enty-five or seventy-six years. It was impossible 
now to doubt that they were the periods of a revolv- 
ing body, its orbit a long ellipse, not a parabola. If 
this were so, the comet must reappear in 1758 or 
1759. Halley began his laborious calculations and 
predicted that the comet would reach its perihelion 
April 13, 1759, but claimed the license of a month 
for the inevitable inaccuracies of a calculation in 
which, in addition to all other sources of error, was 
made in haste, that it might appear as a prediction. 
The comet justified his calculations and his caution 
together ; for it arrived at its perihelion on March 
13, 1759." J 

Another illustration of a like nature is the pre- 
diction of Faraday, based upon Wheatstone's ex- 
perimental proof that the conduction of electricity 
required time ; namely, " that if the conducting 
wires were connected with the coatings of a large 
Leyden jar, the rapidity of conduction would be 
necessarily lessened. This prediction was made in 
1838 and was not verified until, sixteen years later, 
a submarine cable was laid beneath the English 
Channel. A considerable retardation of the electric 
spark was then detected by Siemens and Latimer 
Clark. Faraday at once pointed out that the wire 
surrounded by water resembles a Leyden jar on a 
large scale : so that each message sent through the 
cable verified his remark of 1838." 2 

In Pasteur's experiments with silkworms already 
referred to, he made a prediction in 1866, when, 

1 Whewell, History of Inductive Science, 3d ed. Vol. II. p. 182. 

2 Jevons, Principles of Science, p. 543. 



VERIFICATION AND PREDICTION 161 

having inspected fourteen parcels of eggs intended 
for incubation, and having examined the moths 
Which produced these eggs, he wrote out the pre- 
diction of what would occur in 1867, and placed 
the prophecy as a sealed letter in the hands of the 
mayor of St. Hippolyte. In 1867, the cultivators 
communicated to the mayor their results. The 
letter of Pasteur was then opened and read, and it 
was found that in twelve out of fourteen cases 
there was absolute conformity between his predic- 
tion and the observed facts. Many of the groups 
had perished totally ; the others had perished 
almost totally ; and such was Pasteur's prediction. 
In two out of the fourteen cases, instead of the 
prophesied destruction, half an average crop was 
obtained. 1 

Another interesting illustration concerns Dar- 
win's speculations regarding the formation of coral 
reefs and atolls. Before Darwin wrote on the 
subject, it was generally believed that the coral 
atolls were formed by the coral polypes growing 
upon submerged volcanic craters. Darwin insisted 
that as the polypes cannot live below a depth of 
100 feet, and are killed by exposure to sunshine and 
air, and could not therefore have grown upward 
from the vast depths to which the coral masses 
extend, each atoll must have begun as a fringing- 
reef about an island almost touching the shore, with 
only a narrow and shallow channel of water be- 
tween ; and then became a barrier reef, that is, one 
with a wider and deeper channel of water separat- 

1 Tyndall, Fragments of Science, pp. 291, 292. 



162 INDUCTIVE LOGIC 

ing from the shore, owing to the slow but progres- 
sive subsidence of the island round which the 
polypes first began to build. Then with the further 
and complete subsidence of the island beneath the 
water, there remained a ring of coral with a central 
lagoon forming the so-called atoll. Darwin says in 
his Autobiography that the main features of his 
theory were conceived while on the voyage, and 
that even previous to seeing a true coral reef. 1 He 
says : " No other work of mine was begun in so 
deductive a spirit as this, for the whole theory was 
thought out on the west coast of South America, 
before I had seen a true coral reef. I had only to 
verify and extend my views by a careful examina- 
tion of living reefs. But it should be observed 
that I had during the two previous years been in- 
cessantly attending to the effects on the shores of 
South America of the intermittent elevation of the 
land, together with denudation and deposition of sedi- 
ment. This necessarily led me to reflect much on the 
effects of subsidence, and it was easy to replace in 
imagination the continued deposition of sediment 
by the upward growth of corals. To do this was 
to form my theory of the formation of barrier reefs 
and atolls." 

It will thus be seen that Darwin's deduction was 
based upon previous inductions in other spheres, 
the result of his own observation; he also tells us 
in the same connection, that he had, in the prepa- 
ration of his work on Coral Reefs, spent twenty 
months of hard labor, reading every work on the 

1 Life and Letters of Charles Darwin, 1887, Vol. I. p. 58. 



VERIFICATION AND PREDICTION 163 

islands of the Pacific and consulting many charts. 
He thus made the widely extended observations of 
other men tributary to his inferences concerning 
coral-reef formations. Dr. Williams says of Dar- 
win's insight in this particular : " He saw more 
clearly than his precursors had done the validity 
of the dictum of Johannes Muller in this, and 
indeed all his works, that the most important 
truths in natural science are to be discovered, 
neither by the mere analysis of philosophical ideas, 
nor by simple experience, but by reflective experience, 
which distinguishes the essential from the acciden- 
tal in the phenomena observed, and thus finds 
principles from which many experiences can be 
derived." l This is a very satisfactory and strik- 
ing account of what may be styled the combined 
inducto-deductive temper of mind, and especially 
as embodied in so eminent a student of nature as 
Darwin. 

Bacon insists that anticipations of nature are 
sources of innumerable errors, and that the truly 
scientific method consists in an interpretation of 
nature as it is revealed to the perception through 
direct observation and experiment. It is, however, 
largely through these " anticipations " that progress 
in science is attained. There may be anticipations 
which are considered final, and all attempts at veri- 
fication regarded as unnecessary and even as im- 
pertinent. Results deductively attained are then 
asserted with dogmatic insistence, as though pos- 

1 Darwin, Coral Reefs. Prefatory note by Dr. J. W. Williams, 
p. ix. 



164 INDUCTIVE LOGIC 

sessing the convincing power of facts themselves; 
and all appeal to controverting or exceptional cases 
are set aside, without even so much as a respectful 
hearing. Such anticipations of nature rightfully 
fall under the scornful reprehension of a Bacon. 
But there are other anticipations which serve as 
a spur to a more penetrating observation, and more 
painstaking experiment, in order to square theory to 
facts. Such anticipations are the glory of science ! 
Suppose such anticipations are disproved by 
subsequent experiment or observation ; they have 
served a high purpose in suggesting investigation 
along lines which otherwise would have remained 
unthought of. Anticipations alone are barren ; an- 
ticipations leading to verification are productive of 
valuable results. To this the history of scientific 
thought bears abundant testimony. Professor Clif- 
ford has made the power of prediction one of the 
essential characteristics of scientific thought. He 
says, in his essay on the Aims and Instruments of 
Scientific Thought, that "the difference between sci- 
entific and merely technical thought is just this : 
Both of them make use of experience to direct hu- 
man action; but while technical thought or skill 
enables a man to deal with the same circumstances 
that he has met with before, scientific thought en- 
ables him to deal with different circumstances that 
he has never met with before." 1 He cites two illus- 
trations, which are admirable examples of scientific 
prediction. The first relates to the suggestion of 
Fleeming Jenkin, regarding structural bracing. It 

1 Clifford, Lectures and Essays, Vol. I. p. 128. 



VERIFICATION AND PREDICTION 165 

had been knoAvn before that in an arch every part 
is compressed or pushed by other parts ; and every 
part of a chain is in a state of tension, that is, 
pulled by the other parts. In many cases these 
forms are united in the common girder, which con- 
sists of two main pieces, of which the upper acts 
as an arch, and is compressed, while the lower one 
acts as a chain and is pulled. " Now," says Profes- 
sor Clifford, '■ suppose that any good, practical engi- 
neer makes a bridge or a roof upon some approved 
pattern which has been made before. He designs 
the size and shape of it to suit the opening which 
has to be spanned ; selects his material according 
to the locality ; assigns the strength which must be 
given to the several parts of the structure, accord- 
ing to the load which it will have to bear. There 
is a great deal of thought in the making of this 
design, whose success is predicted by the applica- 
tion of previous experience ; it requires technical 
skill of a very high order, but it is not scientific 
thought. On the other hand, Mr. Fleeming Jenkin 
designs a roof consisting of two arches braced to- 
gether, instead of an arch and a chain braced 
together; and, although this form is quite different 
from any known structure, yet before it is built he 
assigns with accuracy the amount of material that 
must be put into every part of the structure in 
order to bear the required load, and this prediction 
may be trusted with perfect security. What is the 
natural comment on this ? Why, that Mr. Fleeming 
Jenkin is a scientific engineer." 1 

i Clifford, Lectures and Essays, Vol. I. pp. 127, 128. 



166 INDUCTIVE LOGIC 

The second illustration which Professor Clifford 
gives is as follows : " You know that if you make a 
dot on a piece of paper, and then hold a piece of 
Iceland spar over it, you will see not one dot, but 
two. A mineralogist, by measuring the angles of a 
crystal, can tell you whether or no it possesses this 
property without looking through it. He requires 
no scientific thought to do that. But Sir William 
Rowan Hamilton, the late astronomer royal of Ire- 
land, knowing these facts, and also the explanation 
of them, which Fresnel had given, thought about the 
subject, and he predicted that by looking through 
certain crystals in a particular direction we should 
see not two dots, but a continuous circle. Mr. Lloyd 
made the experiment and saw the circle, a result 
which had never been even suspected. This has 
always been considered one of the most signal 
instances of scientific thought in the domain of 
physics. It is most distinctly an application of 
experience gained under certain circumstances to 
entirely different circumstances." 1 

There is also an indirect method of prediction, 
varying somewhat from the one already described 
and yet similar to it. It is called prediction by 
inversion of cause and effect. There are many 
cases in which cause and effect are related in a 
reciprocal manner, so that not only will the cause 
produce the effect, but the effect, operating as a 
cause, will bring about the original cause as an 
effect, it may be in a modified form but clearly recog- 
nizable as such. Professor Tyndall said of Faraday 

1 Clifford, Lectures and Essays, Vol. I. pp. 128, 129. 



VERIFICATION AND PREDICTION 167 

that " the strong tendency of his mind to look upon 
the reciprocal actions of natural forces gave birth 
to his greatest discoveries." J For instance, Oersted 
had proved that an electric current will produce 
magnetism, and Faraday, taking this as a suggestion, 
inferred that magnetism might produce an electric 
current ; in the year 1831 he devised a suitable 
experiment of introducing a bar-magnet into a coil 
of insulated copper wire, and then withdrawing the 
magnet whilst the two ends of the wire were con- 
nected with a distant galvanometer, which indicated 
the presence of the electric current. Thus, his in- 
ference received substantial verification. 2 

It has, moreover, been found that when a given 
cause produces a certain effect, then if the effect be 
produced in some other manner, the process will tend 
to produce the original cause, but inverted as regards 
its direction or nature. For instance, it is known 
that heat will expand gases ; now, if a gas be re- 
lieved of the pressure of the vessel enclosing it, it will 
expand by virtue of its own elastic power, produc- 
ing, however, cold in the surrounding atmosphere. 
So also heat will cause a bar of iron to expand. 
Dr. Joule proved that if iron were expanded by 
mechanical force, it would be accompanied by cold. 
Inasmuch as india-rubber is related to heat in an 
opposite manner to that of iron, being contracted 
by heat instead of expanded, we would, according 
to the law above expressed, naturally expect that 
a mechanical expansion of india-rubber would give 

1 Tyndall, Fragments of Science, p. 338. 

2 Gore, The Art of Scientific Discovery, p. 594. 



168 INDUCTIVE LOGIC 

heat, and a contraction produce cold. An experi- 
ment may be tried by suddenly stretching a rubber 
band while the middle part is in the mouth ; when 
stretched, it grows warm ; when relaxed, it seems 
cold. 1 

Again, as heat will melt many substances, if we 
can reduce the same substance from the solid to 
the liquid state, we would expect, as a result, the 
negative of heat, namely, cold. This occurs in all 
freezing mixtures, as the affinity of salt for water 
causes it to melt ice, thus producing cold in the 
surrounding atmosphere, sufficient to freeze cream 
or other similar substance, inasmuch as, passing 
from solid to liquid, water absorbs heat from all 
substances near it ; this absorption producing arti- 
ficial cold surrounding it. The reciprocal action 
of heat and cold is illustrated in an interesting ex- 
periment described by Tait. 2 He took a bar of ice, 
supported horizontally at either end, and over the 
middle of the bar he put a fine wire, and put equal 
weights to the two ends of the wire. The wire 
gradually, by the action of the weights, cut through 
the bar of ice, and yet it was observed that the path 
of the wire was instantly replaced by the freezing 
again of the melted portion produced by the press- 
ure, and when the wire had wholly traversed the 
entire thickness of the bar, the bar itself was intact, 
and even stronger along the line of the cutting than 
before. The explanation of this experiment is that 
inasmuch as heat melts ice, then when ice is melted 

1 Jevons, Principles of Science, p. 545. 

2 Tait, Recent Advances in Physical Science, pp. 99, 100. 



VERIFICATION AND PREDICTION 169 

by pressure, as in this case of the weighted wire, 
cold, the negative of heat, is induced ; thus, as the 
wire was forced by the weights into the ice, the press- 
ure upon the ice melted it, making it colder, so that 
the water produced, passing around the chilled wire, 
and being thus relieved of pressure, froze again. 

Faraday predicted certain magnetic phenomena 
by this method, which are specially interesting 
as illustrations of this kind of prediction. It 
seems that Arago had observed in 1824 that the 
number of oscillations which a magnetized needle 
makes in a given time, under the influence of 
the earth's magnetism, is very much lessened by 
the proximity of certain metallic masses, and es- 
pecially of copper. Employing the latter substance 
in an experiment upon a magnetized needle, he suc- 
ceeded in reducing the number of its vibrations in 
a given time from three hundred to four. Taking 
the experiment as a basis for his inference, Fara- 
day predicted that since the presence of a metal at 
rest stops the oscillations of a magnetic needle, the 
neighborhood of a magnet at rest ought to stop 
the motion of a rotating mass of metal. He there- 
fore proceeded to put his inference to the test of 
actual experiment, by suspending a cube of copper 
to a twisted thread which was placed between the 
poles of a powerful electromagnet. When the 
thread was left to itself, it began to spin round 
with great velocity, but stopped the moment a 
powerful current passed through the electromag- 
net. 1 Again, as heat applied to the junction of 

l Ganot, Phijsics, pp. 797, 798. 



170 INDUCTIVE LOGIC 

two metallic bars, as antimony and bismuth, pro- 
duced an electric current, it was inferred that if an 
electric current was made to pass through such a 
junction, it would produce cold, and such proved to 
be the case. 1 

In the general process of verification, it often 
happens that seeming exceptions occur which are 
direct contradictions of the law we are attempting 
to prove. And it is in dealing with such cases 
that one's power of discrimination is most fully 
taxed. It is necessary to make a most careful 
distinction between seeming and real exceptions. 
Professor Jevons has given a very exhaustive clas- 
sification of the different kinds of exceptional 
phenomena, which it is well to have in mind, in 
order to know in any investigation the various pos- 
sible complications that may rise. 2 The excep- 
tional phenomena, as given by Jevons, are : — 

1. Imaginary, or false exceptions ; that is, facts, 
objects, or events which are not really what they 
are supposed to be. 

2. Apparent but congruent exceptions, which, 
though apparently in conflict with a law of nature, 
are really in agreement with it. 

3. Singular exceptions, which really agree with 
a law of nature, but exhibit remarkable and unique 
results of it. 

4. Divergent exceptions, which really proceed 
from the ordinary action of known processes of 

1 Jevons, Principles of Science, p. 547. 

2 See Jevons, Chapter XXIX., in his Principles of Science, on 
" Exceptional Phenomena." 



VERIFICATION AND PREDICTION 171 

nature, but which are excessive in amount or 
monstrous in character. 

5. Accidental exceptions, arising from the inter- 
ference of some entirely distinct but known law of 
nature. 

6. Novel and unexplained exceptions, which lead 
to the discovery of a new series of laws and phe- 
nomena, modifying or disguising the effects of pre- 
viously known laws without being inconsistent 
with them. 

7. Limiting exceptions, showing the falsity of 
a supposed law to some cases to which it had been 
extended, but not affecting its truth in other cases. 

8. Contradictory, or real, exceptions, which lead 
us to the conclusion that a supposed hypothesis or 
theory is in opposition to the phenomena of nature, 
and must therefore be abandoned. 

It will be seen that among so many possibilities 
of interpretation an exception does not necessarily 
prove the rule, as the old adage would have it; 
nor does the exception, on the other hand, neces- 
sarily disprove the rule or law. It must be in each 
case strictly and adequately interpreted, which re- 
quires a penetrating sagacity and a thorough knowl- 
edge of the phenomena under investigation. 

In the process of verification, the question nat- 
urally suggests itself: How many verifying in- 
stances are sufficient to determine the universal 
validity of a given law ? This question will be 
recognized as an old difficulty, now presented in 
another form ; but in reality it is the perplexing 
problem of determining the logical ground of in- 



172 INDUCTIVE LOGIC 

duction. What is our warrant for proceeding from 
known and verified instances to unknown phenom- 
ena, of the same kind it is true, but as yet beyond 
the pale of our experience ? The warrant for our 
generalization does not lie wholly in the number of 
verifying instances. In addition to the effect which 
mere number produces in confirming our belief, 
there is the confidence which we feel in the con- 
stancy of the order of nature, and which we are 
constrained to assume as a fundamental postulate. 1 
Therefore, we say that the verifying facts must be 
of such a number, and of such a nature as well, 
that they give evidence of a uniformity which 
transcends all supposition of mere coincidence, and 
compels us to attribute it to the uniformity of 
nature itself, in which we find a warrant for our 
generalization. As Professor Clifford has remarked : 
" The aim of scientific thought is to apply past ex- 
periences to new circumstances. The instrument 
is an observed uniformity in the course of events. 
By the use of this instrument it gives us informa- 
tion transcending our experience, it enables us to 
infer things that we have not seen from things 
that we have seen ; and the evidence for the truth 
of that information depends on our supposing that 
the uniformity holds good beyond our experience." x 
In extending knowledge and predicting results 
beyond the sphere of experience, modern scientific 
investigation is largely indebted to the principles 
and methods of mathematics. Mathematical laws, 

i See Sigwart, Logic, Vol. II. p. 348. 

2 Clifford, Lectures and Essays, Vol. I. pp. 131, 132. 



VERIFICATION AND PREDICTION 173 

applied to the data given in sense-perception, give 
indications of the necessary relations that must 
exist in the observed phenomena, and all that they 
involve. Thus, that which is given directly in con- 
sciousness is supplemented by that which is given 
indirectly as mathematically necessitated. The 
mathematico-experimental method in physics has 
led to very rich and important results which have 
proved practically its efficiency as a scientific 
method. 



CHAPTER XIII 

Hypothesis 

The inductive process cannot proceed to any- 
great extent or attain satisfactory results without 
the aid of some hypothesis. An hypothesis is a 
supposition regarding the cause of a phenomenon, 
which we make either as preliminary to an experi- 
ment which will prove or disprove the supposition, 
or in lieu of an experiment or systematic observa- 
tion when such are impossible, owing to the peculiar 
conditions of the phenomenon itself. We see, there- 
fore, that the framing of hypotheses has a double 
function. First, considered as preliminary to ex- 
periment. We found that in cases where two, three, 
or more elements enter into a complex antecedent, it 
is impossible often, and always impracticable to test 
the various possible combinations separately in order 
to note their different results. The combinations in 
complex phenomena are indefinitely great, and the 
isolation of certain elements in order to estimate 
the exact result of the combined force of the other 
combinations is extremely difficult and often im- 
possible. Therefore the mind discards some com- 
binations as irrelevant, others as impossible, and 
selects one perhaps as the most likely cause of the 
174 






HYPOTHESIS 175 



given effect. This selective function of the mind, 
therefore, indicates the line of experiment in a de- 
terminate manner and does not leave the phenom- 
ena to indeterminate and haphazard investigation. 
Consider, for instance, so eminent an experimenter 
as Charles Darwin, so fertile in all kinds of experi- 
mental resources ; yet it is said of him that every 
experiment was the result of a tentative theory, 
thought out in advance of all actual test by a saga- 
cious insight into the necessary conditions of the 
interrelated phenomena before him. His son, Fran- 
cis Darwin, says of him in his Reminiscences: "He 
often said that no one could be a good observer 
unless he was an active theorizer. It was as though 
he were charged with theorizing power ready to 
flow into any channel on the slightest disturbance, 
so that no fact, however small, could avoid releasing 
a stream of theory, and thus the fact became mag- 
nified into importance. In this way, it naturally 
happened that many untenable theories occurred to 
him ; but fortunately his richness of imagination 
was equalled by his power of judging and condemn- 
ing the thoughts that occurred to him. He was 
just to his theories, and did not condemn them un- 
heard ; and so it happened that he was willing to 
test what would seem to most people not at all 
worth testing. These rather wild trials he called 
i fool's experiments,' and enjoyed extremely. As an 
example, I may mention that, finding the cotyledons 
of Biophytum to be highly sensitive to vibrations 
of the table, he fancied that they might perceive 
the vibrations of sound ; and therefore made me play 



176 INDUCTIVE LOGIC 

my bassoon close to a plant. The love of experiment 
was very strong in him, and I can remember the way 
he would say, ' I shan't be easy till I have tried it,' 
as if an outside force were driving him." 1 

Hypothesis and experiment were in the hand of 
Darwin like a two-edged sword, which he employed 
with rare skill and effect. An hypothesis is to be 
regarded not only as the precursor of experiment, 
but it also functions as a method of explanation 
when actual verification is impossible. We see 
this constantly in our every-day life. We are com- 
pelled again and again to account for situations 
which occur that are impossible for us to reproduce 
in the form of an experiment, that we are able to 
observe but once. Some explanation is required to 
satisfy mental demands which are imperative in 
this regard. The explanation which seems most in 
keeping with the sum of facts in our possession, is 
the hypothesis which we frame ; so also in explain- 
ing the conduct of others by conjecture as to the 
most reasonable motives that will satisfactorily 
account for the same ; such hypotheses we are con- 
stantly compelled to assume. We are not always 
able to perceive the relations existing between 
facts as they come into the sphere of our experi- 
ence, and yet we are constrained to think of them 
as related; but in order to systematize them, we 
must supply mentally the lacunce which appear in 
the phenomena as perceived. This supposition that 
is necessary to construct facts into system is an 
hypothesis. 

1 Life and Letters of Charles Darwin, Vol. I. p. 126. 



HYPOTHESIS 177 

An illustration of an hypothesis suggesting syste- 
matic observation and experiment is found in the 
history of the discovery of vaccination by Jenner. 
It seems that while a mere youth, pursuing his 
studies at Sodbury, he chanced to hear a casual 
remark made by a country girl who came to his 
master's shop for advice. The small-pox was men- 
tioned, when the girl said, " I cannot take that dis- 
ease, for I have had cow-pox." 1 This observation, 
expressing the common superstition of the simple 
country folk, appealed to Jenner's mind as an in- 
choate hypothesis. Seizing upon it as a suggestion 
of possible value, he proceeded to make diligent 
inquiries and careful observations, which finally 
led him to the discovery of vaccination. 

An illustration of hypothesis as explanation of 
phenomena beyond the range of experiment is found 
in the hypothesis as to the source of the sun's 
energy. An enumeration of the different hypothe- 
ses advanced upon this subject is given by Tait in 
his Recent Advances in Physical Science. 2 "The 
old notion that the sun is a huge fire, or something 
of that kind, is one which will only occur to one 
thinking of the matter for the first time ; but with 
our modern chemical knowledge, we are enabled to 
say that, massive as the sun is, if its materials had 
consisted of the very best materials for giving out 
heat, that enormous mass of some 400,000 miles 
in radius could have supplied us with only about 
5000 years of the present radiation. A mass of 

1 Gore, The Art of Scientific Discovery, p. 495. 

2 pp. 151 ff . 

N 



178 INDUCTIVE LOGIC 

coal of that size would have produced very much 
less than that amount of heat. Nor would the 
most energetic chemicals known to us, combined 
in proportion for giving the greatest amount of 
heat by actual chemical combination, supply the 
sun's present waste for even 5000 years. There- 
fore as we all know that geological facts, if there 
were no others, point to at least as high a radiation 
from the sun as the present, for at all events a few 
hundreds of thousands of years back, — and per- 
haps also indicate even a higher rate of radiation 
from the sun in old time than at present, — it is 
quite obvious that the heat of the sun cannot 
possibly be supplied by any chemical process of 
which we have the slightest conception. 

"Now, if we can find, on the other hand, any 
physical explanation of this consistent with any 
present knowledge, we are bound to take it and use 
it as far as we can, rather than say : This question 
is totally unanswerable unless there be chemical 
agencies at work in the sun of a far more power- 
ful order than anything we meet with on the 
earth's surface. If we can find a thoroughly in- 
telligible source of heat, which, though depending 
upon a different physical cause from the usual 
one, combustion, is amply sufficient to have sup- 
plied the sun with such an amount of heat as to 
enable it to radiate for perhaps the last hundred 
millions of years at the same rate as it is now 
radiating, then I say we are bound to try that 
hypothesis first, and argue upon it until we find it 
inconsistent with something known. And if we 



HYPOTHESIS 179 

do not find it inconsistent with anything that is 
known, while we find it completely capable of 
explaining our difficulty, then it is not only philo- 
sophic to say that it is most probably the origin 
of the sun's energy, but we feel ourselves con- 
strained to admit it. Newton long ago told us 
this obligation in his Rules of Philosophizing. 
Now it is known that if we were to take a mass 
of the most perfect combustibles which we know, 
and let it fall upon the sun merely from the 
earth's distance, then the work done upon it by 
the sun's attraction during its fall would give it so 
large an amount of kinetic energy when it reached 
the sun's surface as to produce an impact which 
would represent six thousand times the amount of 
energy which could be produced by its mere burn- 
ing. 

"It appears, then, that our natural and only 
trustworthy mode of explaining the sun's heat at 
present, in time past, and for time to come must be 
something closely analogous to, but not identical 
with, what was called the nebular hypothesis of 
Laplace, — the hypothesis of the falling together 
(from rudely scattered distribution in space) of 
the matter which now forms the various suns and 
planets. We find by calculation in which there is 
no possibility of large error, that this hypothesis 
is thoroughly competent to explain one hundred 
millions of years' solar radiation at the present 
rate, perhaps more ; and it is capable of showing 
us how it is that the sun, for thousands of years 
together, can part with energy at the enormous 



180 INDUCTIVE LOGIC 

rate at which it does still part with it, and yet 
not apparently cool by perhaps any measurable 
quantity. 

"In confirmation of this, not only is the hy- 
pothesis itself capable of explaining the amounts 
of energy which are in question, but also recent in- 
vestigations, aided by the spectroscope, have shown 
us that there are gigantic nebular systems at great 
distances from our solar system, in the process of 
physical degradation in that very way, by the 
falling together of scattered masses, and with 
numerous consequent developments of heat by 
impacts. What are called temporary stars form 
another splendid and still more striking instance 
of it, as where a star suddenly appears, of the first 
magnitude, or even brighter than the first, out- 
shining all the planets for a month or two at a 
time, and then, after a little time, becomes invisi- 
ble in the most powerful telescope. Things of 
that kind are constantly occurring on a larger or 
smaller scale and they can all be easily explained 
on this supposition of the impact of gravitating 
masses." 

Such a hypothesis, it will be seen, embraces all 
the facts observed in one self-consistent system. 
The other hypotheses are inadequate to account 
satisfactorily for the phenomena. The validity 
of this hypothesis lies in its being both adequate 
and congruent as well ; experiment or corroborative 
observation being out of the question, we are, as 
Tait says, " constrained to admit it." 

Mr. Darwin gives an enumeration and criticism 



HYPOTHESIS 181 

of the different hypotheses which have been sug- 
gested to explain the extinction of the gigantic 
animals known to have existed upon the earth. 
His account will give an indication of the natural 
propensity of the mind to frame hypotheses con- 
cerning phenomena which lie outside the sphere 
both of observation and experiment. Mr. Darwin 
says: "It is impossible to reflect on the changed 
state of the American Continent without the deep- 
est astonishment. Formerly it must have swarmed 
with great monsters ; now Ave find mere pigmies 
compared with the antecedent allied races. The 
greater number, if not all, of these extinct quad- 
rupeds, lived at a late period, and were the con- 
temporaries of most of the existing sea-shells. 
What then has exterminated so many species and 
whole genera ? The mind at first is irresistibly 
hurried into the belief of some great catastrophe ; 
but thus to destroy animals, both large and small, 
in Southern Patagonia, in Brazil, on the Cordillera 
of Peru, in North America up to Behring's Straits, 
we must shake the entire framework of the globe. 

"An examination, moreover, of the geology of 
La Plata and Patagonia leads to the belief that 
all the features of the land result from slow and 
gradual changes. It appears from the character 
of the fossils in Europe, Asia, Australia, and in 
North and South America, that those conditions 
which favor the life of the larger quadrupeds 
were lately coextensive with the world. What 
those conditions were, no one has yet even con- 
jectured. It could hardly have been a change of 



182 INDUCTIVE LOCxIC 

temperature, which at about the same time de- 
stroyed the inhabitants of tropical, temperate, and 
arctic latitudes on both sides of the globe. In 
North America we positively know from Mr. Lyell 
that the large quadrupeds lived subsequently to 
that period when boulders were brought into lati- 
tudes at which icebergs now never arrive; from 
conclusive but indirect reasons we may feel sure 
that in the southern hemisphere the Macrauchenia 
also lived long subsequently to the ice-transporting 
boulder-period. Did man, after his first inroad 
into South America, destroy, as has been suggested, 
the unwieldy Megatherium and the other Eden- 
tata ? We must look at least to some other cause 
for the destruction of the little tucutuco at Bahia 
Blanca, and of the many fossil mice and other 
small quadrupeds in Brazil. No one will imagine 
that a drought, even far severer than those which 
cause such losses in the provinces of La Plata, 
could destroy every individual of every species 
from Southern Patagonia to Behring's Straits. 
What shall we say of the extinction of the horse ? 
Did those plains fail of pasture which have since 
been overrun by thousands and hundreds of thou- 
sands of the descendants of the stock introduced 
by the Spaniards ? Have the subsequently intro- 
duced species consumed the food of the great 
antecedent races ? Can we believe that the Capy- 
bara has taken the food of the Toxodon, the 
Guanaco of the Macrauchenia, the existing small 
Edentata of their numerous gigantic prototypes ? 
Certainly no fact in the long history of the world 



HYPOTHESIS 183 

is so startling as the wide and repeated exter- 
minations of its inhabitants." x Mr. Darwin's own 
hypothesis concerning this phenomenon is rather 
indefinite, but nevertheless as definite as the ex- 
treme complexity of the facts will allow. He 
says that there are certain causes operating in 
nature, their exact character remaining unknown, 
such that the too rapid increase of every species, 
even the most favored, is steadily checked, pro- 
ducing in some cases rarity and in others ex- 
tinction, if these causes operate with unusual 
efficacy. His hypothesis marks a tendency whose 
nature, nevertheless, remains concealed. 

In all these widely differing hypotheses we see a 
certain mental constraint to offer some explanation, 
even though it be but a disguised confession of 
ignorance, as in Mr. Darwin's hypothesis. 

An illustration of an hypothesis to explain ob- 
served phenomena that cannot be further tested is 
that given in the following instance cited by Pro- 
fessor Tyndall : " At Erith, in 1864, there occurred 
a tremendous explosion of a powder magazine. The 
village of Erith was some miles distant from the 
magazine, but in nearly all cases the windows were 
shattered ; and it was noticeable that the windows 
turned away from the origin of the explosion suf- 
fered almost as much as those which faced it. Lead 
sashes were employed in Erith church ; and these, 
being in some degree flexible, enabled the windows 
to yield to pressure without much fracture of glass. 
Every window in the church, front and back, was 
1 Darwin, Voyage, of a Naturalist, Vol. I. p. 223. 



184 INDUCTIVE LOGIC 

bent inwards. In fact, as the sound-wave reached 
the church, it separated, right and left, and, for a 
moment, the edifice was clasped by a girdle of in- 
tensely compressed air, which forced all its win- 
dows inwards. After compression, the air in the 
church no doubt dilated, and tended to restore the 
windows to their first condition. The bending in 
of the windows, however, produced but a small 
condensation of the whole mass of air within the 
church; the force of the recoil was, therefore, 
feeble in comparison with the force of impact, 
and insufficient to undo what the latter had ac- 
complished." l Here also is a set of conditions 
that must be satisfied by a correct hypothesis. 
The phenomenon was not capable of repetition by 
any experiment. Professor Tyndall, therefore, pict- 
ures to his mind what must have happened beyond 
that which was observed, in order to account for 
the result which actually happened. He fills up 
the unseen from what he knows of the nature of 
sound-waves, and thus constructs one self-consistent 
system which includes both the seen and the un- 
seen, the known and the unknown, the observed 
and the inferred. 

It will be noticed in this and other illustrations 
of hypothesis, how large a part is played by the 
imagination. It is the imagination which fills out 
the vacant spaces in the picture of perception. 
With some, the function of imagination is asso- 
ciated with fancy rather than fact. It must, in 
this connection, however, be clearly emphasized 

i Tyndall, On Sound, p. 23. 



HYPOTHESIS 1 85 

that the imagination which constructs hypotheses 
must be throughout in touch with fact. It must 
represent to the mind, not what fancy suggests, but 
what the known facts necessitate. The unseen is 
constructed out of the determining conditions of 
the seen. It is this deductive function of the 
imagination that gives to it a strictly logical sig- 
nificance. For instance, Professor Tyndall's reason- 
ing concerning the Erith church was somewhat as 
follows : The windows are all bent inward, there- 
fore the pressure must have operated on all sides 
from without, inward ; such pressure could only 
occur upon the supposition that the sound-waves, 
separating right and left, wholly encompassed the 
church, etc. In each case, that which he pictured 
to his mind as happening, was regarded by him as 
actually necessitated by the facts as observed. 

Professor Tyndall has- most admirably discussed 
the " Scientific Use of the Imagination ; " and his 
lecture under that title every student, both of logic 
or of science, should read. I cpiote one passage 
from it, which has special bearing upon what has 
just been said : " We are gifted with the power of 
Imagination, — combining what the Germans call 
Anschauungsgabe and EinbildungsTxraft, — and by 
this power we can lighten the darkness which sur- 
rounds the world of the senses. There are tories 
in science who regard imagination as a faculty to 
be feared and avoided rather than employed. They 
had observed its action in weak vessels and were 
unduly impressed by its disasters. But they might 
with ecpial justice point to exploded boilers as an 



186 INDUCTIVE LOGIC 

argument against the use of steam. Bounded and 
conditioned by co-operant Reason, imagination be- 
comes the mightiest instrument of the scientific dis- 
coverer. Newton's passage from a falling apple 
to a falling moon was, at the outset, a leap of the 
imagination. When William Thomson tries to 
place the ultimate particles of matter between his 
compass points, and to apply to them a scale of 
millimetres, he is powerfully aided by this faculty. 
And in much that has been recently said about 
protoplasm and life, we have the outgoings of the 
imagination guided and controlled by the known 
analogies of science. In fact, without this power 
our knowledge of nature would be a mere tabula- 
tion of coexistences and sequences. We should 
still believe in the succession of day and night, of 
summer and winter ; but the soul of Force would 
be dislodged from our universe ; causal relations 
would disappear, and with them that science 
which is now binding the parts of nature to an 
organic whole." x 

In all the illustrations which have been given, 
and, in fact, in all examples of the framing of 
hypotheses, it will be seen that the mental functions 
specially in operation are those of analysis and 
synthesis, — a separation of the elements as far as 
possible into their simplest forms of expression, 
and the building them together into some one sys- 
tem whose unity lies in the assumed hypothesis. 
Mr. Venn has especially emphasized this aspect of 

1 Tyndall, Use and Limit of the Imagination in Science, 
p. 16. 



HYPOTHESIS 187 

hypothesis, and his chapter on this subject will 
well repay a careful reading. 1 

Every supposition, however, is not necessarily an 
hypothesis in the logical or scientific significance 
of that term. It will be necessary, therefore, to 
mention some of the requirements which a logical 
hypothesis should satisfy. 

1. An hypothesis should be plausible ; that is, it 
should be no fanciful, or merely conjectural, expla- 
nation of the phenomena in question. The sup- 
positions of the interference of spirits, or in a 
mythological age of the gods, to account for per- 
plexing situations or obscure happenings, have no 
rank as hypotheses ; so, also, Fate is often referred 
to as a convenient confession of ignorance in lieu of 
a satisfactory explanation. Spinoza has remarked 
upon this as follows : " They who have desired to 
find scope for the display of their ingenuity in 
assigning causes, have had recourse to a new style 
of argument to help them in their conclusions, 
namely, by reduction, not to the impossible or ab- 
surd, but to ignorance or the unknown, a procedure 
which shows very plainly that there was no other 
course open to them." 

The difference between a scientific hypothesis 
and a popular explanation concerning the same 
phenomena may be found in Darwin's account of 
"a strange belief which is general amongst the 
inhabitants of the Maldiva atolls, namely, that 
corals have roots, and therefore that if merely 
broken down to the surface, they grow up again ; 

1 Venn, Empirical Logic, Chapter XVI. 



188 INDUCTIVE LOGIC 

but if rooted out, they are permanently destroyed. 
By this means the inhabitants keep their harbors 
clear ; and thus the French governor of St. Mary's 
in Madagascar ' cleared out and made a beautiful 
little port at that place.' " 1 Their explanation, 
however, is purely fanciful, having no basis in fact. 
In contrast, Darwin's hypothesis to explain the 
facts in the case is of a logically scientific nature, 
and is as follows : Inasmuch as loose sediment is 
injurious to the living polypifers, and as it is prob- 
able that sand would accumulate in the hollows 
formed by tearing out the corals, but not on the 
broken and projecting stumps, therefore in the 
former case the fresh growth of coral might be 
thus prevented by the deposited sediment. 

2. The second requirement is that the hypothesis 
must be capable of proof or disproof. This does 
not demand a test by experiment necessarily ; for 
that, as we have seen, may be impossible. It does, 
however, require that some facts should be forth- 
coming that will either confirm the hypothesis or 
disprove it. There are cases, however, as Lotze 
suggests, whose very nature precludes the possi- 
bility of proving or disproving the hypothesis 
framed to account for them. For instance, the 
very common and simple hypothesis of regarding 
the stars, which are apparently but small points of 
light, as bodies of vast size, only very remote from 
us, is in itself incapable of being either refuted or 
confirmed by subsequent discovery. Lotze says : 
" We must abide content if our hypotheses are 

1 Darwin, C'oraZ Reefs, p. 89. 



HYPOTHESIS 189 

thinkable and useful, if they are capable of ex- 
plaining all interconnected appearances, even such 
as were still unknown when we constructed them, 
if, that is to say, they are indirectly confirmed by 
the agreement of all that can be deduced from them 
in thought with the actual progress of experience. 
But if we would be so fortunate as to find an 
hypothesis which will not lack this subsequent 
confirmation, we must not simply assume anything 
that can be barely conceived as real ; we must only 
assume that which, besides being thinkable, con- 
forms, so to speak, to the universal customs of real- 
ity, or to the special local customs which prevail in 
that department of phenomena to which the object 
we are investigating belongs." x 

It is to be specially observed that while the re- 
quirement of proof of an hypothesis may be waived 
in the sphere of phenomena where proof is mani- 
festly impossible, still, where proof is available, an 
hypothesis must never be so framed as to render 
the required test either impossible or impracticable. 

3. The hypothesis must be adequate. It must 
cover all the facts in the case. An outstanding 
fact which it cannot explain is sufficient to contro- 
vert such an hypothesis. A knowledge of the dis- 
tinction between postulate and hypothesis, and of 
the relation which nominally exists between the two, 
will help us to appreciate more clearly the force 
of this requirement of adequacy. As defined by 
Lotze, a postulate "expresses the conditions which 
must be set up, or the ground of explanation which 

1 Lotze, Logic, p. 353. 



190 INDUCTIVE LOGIC 

must be given by some reality, force, or event, before 
we can think the phenomenon in the form in which 
it is presented to us ; it thus requires or postulates 
the presence of something that can account for the 
given effect. An hypothesis is a conjecture which 
seeks to fill up the postulate thus abstractly stated 
by specifying the concrete causes, forces, or pro- 
cesses out of which the phenomenon really arose 
in this particular case, while in other cases maybe 
the same postulate is to be satisfied by utterly dif- 
ferent though equivalent combinations of forces or 
active elements." * According to this distinction 
as applied to the problem of the source of the 
sun's energy, the postulate would be the sum of 
conditions which require explanation; namely, the 
tremendous radiation of heat extending through 
thousands and thousands of years. The postulate 
therefore requires a force adequate to supply for so 
long a period so great an amount of energy. We 
found that ordinary combustion of the most highly 
combustible materials would not, as an hypothesis, 
satisfy the conditions which obtain in the postulate ; 
nor would the liberation of chemical energy stand 
as an hypothesis adequate to satisfy the postulate ; 
the hypothesis of impact of masses upon the sun's 
surface from immense distances presents a force 
sufficient to meet the requirements of the postulate. 
Moreover, we see in this illustration how the hy- 
pothesis is a particular and concrete expression of 
the conditions expressed in general and in abstract 
terms in the postulate. The essential characteristic 

1 Lotze, Logic, pp. 349, 350. 



HYPOTHESIS 191 

therefore of the hypothesis is that it shall perfectly 
satisfy all the conditions expressed in the postulate. 

The hypothesis that nature abhorred a vacuum, in 
order to account for the rise of water in a tube or 
pump, was seen to break down utterly when it was 
found that the water did not rise beyond some 
thirty-three feet. The demand of the postulate in 
the case was a force of precisely such magnitude 
that it would balance a column of water thirty-three 
feet in height. This force, precisely satisfying the 
conditions of the postulate, is found in the hypoth- 
esis that the atmospheric pressure is such a magni- 
tude as to exert a pressure equivalent to a column 
of water some thirty-three feet in height. The 
strength of the hypothesis lies in its exact and 
appropriate fitting into the facts of the problem. 

Another illustration of the fitting of hypothesis 
to postulate, and one where the conditions of the 
postulate are extremely complex, I have chosen 
from Mr. Wallace's work, On Natural Selection: 
" There is a Madagascar orchis — the Angroecum 
sesquipedale — with an immensely long and deep 
nectary. How did such an extraordinary organ 
come to be developed? Mr. Darwin's explanation 
is this. The pollen of this flower can only be 
removed by the base of the proboscis of some very 
large moths, when trying to get at the nectar at the 
bottom of the vessel. The moths with the longest 
probosces would do this most effectually ; they 
would be rewarded for their long tongues by get- 
ting the most nectar ; whilst, on the other hand, the 
flowers with the deepest nectaries would be the best 



192 INDUCTIVE LOGIC 

fertilized by the largest moths preferring them. 
Consequently the deepest-nectaried orchids and the 
longest-tongued moths would each confer on the 
other an advantage in the battle of life. This 
would tend to their respective perpetuation, and 
to the constant lengthening of nectaries and pro- 
bosces. In the Angrcecum sesquipedale it is neces- 
sary that the proboscis should be forced into a 
particular part of the flower, and this would only 
be done by a large moth burying its proboscis to 
the very base, and straining to drain the nectar 
from the bottom of the long tube, in which it occu- 
pies a depth of one or two inches only. Now let 
us start from the time when the nectary was only 
half its present length, or about six inches, and was 
chiefly fertilized by a species of moth which ap- 
peared at the time of the plant's flowering, and 
whose proboscis was of the same length. Among 
the millions of flowers of the Angraecum produced 
every year, some would always be shorter than the 
average, some longer. The former, owing to the 
structure of the flower, would not get fertilized, 
because the moths could get all the nectar without 
forcing their trunks down to the very base. By 
this process alone the average length of the nec- 
tary would annually increase, because the short- 
nectaried flowers being sterile, and the long ones 
having abundant offspring, exactly the same effect 
would be produced as if a gardener destroyed the 
short ones, and sowed the seed of the long ones 
only ; and this we know by experience would pro- 
duce a regular increase of length, since it is this 



HYPOTHESIS 193 

very process which has increased the size and 
changed the form of onr cultivated fruits and 
flowers. But this would lead in time to such an 
increased length of the nectary that many of the 
moths could only just reach to the surface of the 
nectar, and only the few with exceptionally long 
trunks be able to suck up a considerable portion. 
This would Cause many moths to neglect these flow- 
ers, because they could not get a satisfying supply 
of nectar, and if these were the only moths in the 
country the flowers would undoubtedly suffer, and 
the further growth of the nectary be checked by 
exactly the same process which had led to its 
increase. 

" But there are an immense variety of moths, of 
various lengths of proboscis, and as the nectary 
became longer, other and larger species would be- 
come the fertilizers, and would carry on the process 
till the largest moths became the sole agents. Now, 
if not before, the moth would also be affected; for 
those with the longest probosces would get the most 
food, would be the strongest and most vigorous, 
would visit and fertilize the greatest number of 
flowers, and would leave the largest number of 
descendants. The flowers most completely fertil- 
ized by these moths being those which had the 
longest nectaries, there would in each generation 
be, on the average, an increase in the length of the 
nectaries, and also an average increase in the length 
of the probosces of the moths ; and this would be a 
necessary result from the fact that nature ever fluct- 
uates about a mean, or that in every generation 



194 INDUCTIVE LOGIC 

there would be flowers with longer and shorter 
nectaries, and moths with longer and shorter pro- 
bosces than the average. I may here mention that 
some of the large Sphinx moths of the tropics have 
probosces nearly as long as the nectary of Angrce- 
cum sesquipedale. I have carefully measured the 
proboscis of a specimen of Macrosila cluentius from 
South America, in the collection of the British 
Museum, and find it to be nine inches and a quarter 
long. One from tropical Africa (Macrosila mor- 
ganii) is seven inches and a half. A species having 
a proboscis two or three inches longer could reach 
the nectar in the longest flowers of Angrcecum ses- 
quipedale, whose nectaries vary in length from ten 
to fourteen inches. That such a moth exists in 
Madagascar may be safely predicted ; l and natural- 
ists who visit that island should search for it with 
as much confidence as astronomers searched for 
the planet Neptune, — and I venture to predict 
they will be equally successful." 2 

I have given this quotation at length in order to 
indicate not only the fitting of hypothesis to the 
facts observed, but also the large and important 
part performed by the imagination in reproducing 
along parallel lines the natural history of the orchid 
and moth. The hypothesis reaches back over an 
indefinitely long past, by virtue of the necessities 

1 It is interesting to note that since Mr. Wallace wrote the 
ahove, Kirby, in his European Moths and Butterflies, makes 
mention of one of the Sphingidse with a prohoscis twelve inches 
long! 

2 Wallace, On Natural Selection, pp. 271-275. 



HYPOTHESIS 195 

observed in the present, and in accordance with 
well-established analogies and approved inductions. 
The function of the imagination especially promi- 
nent is that of its deductive insight, which is able 
to picture to the mind the inevitable results of this 
and that condition as furnished by the postulate, 
and then to tit such necessitated results into one self- 
consistent system, with nothing left unexplained, 
incongruous, or contradictory. 

Another illustration of an hypothesis covering a 
large number of complex facts is that of the ferti- 
lization of certain flowers by means of the wind. 
As given by Sir John Lubbock, we have the follow- 
ing facts and the corresponding explanation of 
them : " Wind-fertilized flowers, as a rule, have no 
color, emit no scent and produce no honey, and are 
regular in form. Color, scent, and honey are the 
three characteristics by which insects are attracted 
to flowers. Again, as a rule wind-fertilized flowers 
produce much more pollen than those which are 
fertilized by insects. This is necessary, because 
it is obvious that the chances against any given 
pollen grain reaching the stigma are much greater 
in the one case than in the other. Every one has 
observed the showers of yellow pollen produced by 
the Scotch fir. Again, it is an advantage to wind- 
fertilized plants to flower early in the spring before 
the leaves are out, because the latter would catch 
much of the pollen, and thus interfere with its 
access to the stigma. Again, in these plants the 
pollen is less adherent, so that it can be easily 
blown away by the wind, which would be a disad- 



196 INDUCTIVE LOGIC 

vantage in most plants which are fertilized by 
insects. Again, such flowers generally have the 
stigma more or less branched, or hairy, which evi- 
dently must tend to increase their chances of 
catching the pollen." 1 There is here a structural 
adaptation of these plants to the circumstances 
designed to explain them, so that the consequent 
self-consistent system thus formed carries with it 
the weight of conviction. 

There are some explanations which do not per- 
fectly correspond to reality, and yet, when their 
nature is known, they may be profitably used, not 
to represent reality, but to assist the mind by an 
approximate representation to better appreciate the 
facts as they really are related one to another. 
These so-called " fictions " are useful, especially in 
mathematics. We suppose, for instance, inscribed 
and circumscribed polygons of a circle, with ever- 
increasing number of sides, gradually approaching 
and becoming coincident finally with the curve 
itself. This latter we know to be impossible, and 
yet we may treat that which happens only approxi- 
mately as though really happening, merely as an 
aid to the imagination ; and a fiction, if always so 
understood, may thus prove helpful in the repre- 
sentation of reality more clearly to our minds. 

4. The hypothesis, moreover, should involve no 
contradiction. This is clearly a requirement that 
is deductive rather than inductive, depending upon 
the fundamental principle of contradiction lying at 
the basis of the deductive system of logic. 
1 Lubbock, Scientific Lectures, pp. 9, 10. 



HYPOTHESIS 197 

5. The hypothesis should be as simple as possible. 
No involved explanation that mystifies rather than 
clears the difficulties presented can rank as a true 
hypothesis. Simplex veri sigillum. This require- 
ment, of course, cannot in all cases be strictly com- 
plied with ; for the phenomena to be explained may 
present such a degree of complexity that a simple 
hypothesis would be altogether out of the question. 
For instance, the hypothesis of a substance filling 
the universe, and pervading all particles of matter, 
however solid and closely knit together, a substance 
itself more solid than steel, and more elastic as well, 
such a supposition seems not only too involved, but 
also even to belie the ordinary judgments of common 
sense. And yet this undulatory hypothesis is more 
and more confirmed by every advance of science in 
the knowledge of the phenomena of light and heat. 

It sometimes happens that the very failure of an 
hypothesis forms a substantial contribution to the 
progress of thought, leading to the readjustment of 
a received theory, or stimulating research in order 
to discover the true in place of the false hypothesis. 
As Mr. Tait says: "We all know that if there 
had not been a pursuit after the philosopher's stone, 
chemistry could not yet have been anything like the 
gigantic science it now is. In the same way we can 
say, that modern physics could not yet have covered 
the ground it now occupies had it not been for this 
experimental seeking for the so-called perpetual 
motion, and the consequent establishment of a defi- 
nite and scientifically useful negative." 1 The cir- 

1 Tait, Recent Advances in Physical Science, p. 69. 



198 INDUCTIVE LOGIC 

cular theory of the orbits of the planets, while 
incorrect, yet made the transition easier from the 
hypothesis of circular motion to that of motion in 
an elliptical orbit, which is the true theory. It 
often happens that an hypothesis may not be 
wholly wrong but may need correction, and this is 
often provided for, not by a total rejection of the 
hypothesis in question, but by supplementing it by 
so-called subsidiary hypotheses. 

As to the tests of a correct hypothesis in addition 
to the fulfilment of the requirements already men- 
tioned, Dr. Whewell has especially emphasized the 
importance of what he has styled a " Consilience of 
Inductions." An hypothesis receives a confirmatory 
strengthening of its validity, when it enables us to 
explain and determine cases not only of the same 
kind as the phenomena out of which the hypothe- 
sis itself has developed, but cases which arise in 
a sphere entirely different from that which gave 
material originally for the formation of the hy- 
pothesis. An hypothesis that can thus be carried 
into new territory as an effective instrument of 
research, is thereby doubly accredited. As Dr. 
Whewell remarks: "Accordingly the cases in 
which inductions from classes of parts altogether 
different have thus jumped together, belong only to 
the best established theories which the history of 
science contains. And as I shall have occasion to 
refer to this peculiar feature in their evidence, I 
will take the liberty of describing it by a particular 
phrase ; and will term it the Consilience of Inchic- 
tions. It is exemplified principally in some of the 



HYPOTHESIS 199 

greatest discoveries. Thus it was found by Newton 
that the doctrine of the attraction of the sun vary- 
ing according to the inverse square of the distance, 
which explained Kepler's Third Law, of the pro- 
portionality of the cubes of the distances to the 
squares of the periodic times of the planets, ex- 
plained also his First and Second Laivs, of the 
elliptical motion of each planet; although no 
connection of these laws had been visible before. 
Again, it appeared that the force of universal gravi- 
tation, which had been inferred from the perturba- 
tions of the moon and planets by the sun and by 
each other, also accounted for the fact, apparently 
altogether dissimilar and remote, of the precession 
of the equinoxes. Here was a most striking and 
surprising coincidence which gave to the theory a 
stamp of truth beyond the power of ingenuity to 
counterfeit." l 

When two rival hypotheses can be submitted to 
the test of an experiment which negatives one and 
confirms the other, such a testing is called an ex- 
perimeutum crucis. The name was first given by 
Bacon, and has met with universal acceptance in 
scientific phraseology. A crucial test, as decisive 
between the emission and the undulatory theory 
of light, is given in an experiment first tried by 
Father Grimaldi, a Bolognese monk, in 1665. If 
a shutter be pierced with a very small hole, and 
the luminous cone which passes through the orifice 
be examined, the cone will be found to be much 

1 Whewell, Novum Organon Renovatum, Bk. II. Ch. V. 
Art. 110. 



200 INDUCTIVE LOGIC 

less acute than would be expected, considering only 
the rectilinear transmission of the rays, as according 
to the emission theory. If there be interposed in 
the path of the luminous ray a second shutter, 
pierced with a hole also, it will be noticed that the 
rays of the second cone are even more divergent 
than those of the first. If the image of the orifice 
be received upon a screen, a white circle is seen 
surrounded by a dark ring, next a white ring, even 
more brilliant than the central portion, then a second 
dark ring, and finally another very faint white ring. 
If in the shutter with which the experiment is 
made, two very small holes are pierced at a dis- 
tance from each other of one or two millimetres, 
and the two images received upon a screen in such 
a manner that they overlap each other, it is found 
that in the cuticular segment formed by the over- 
lapping of the images, the circles are more obscure 
than in the part where they are separated. Thus 
by adding light to light darkness is produced. 1 
These phenomena are now known to be consistent 
only with the undulatory theory, and directly in 
contradiction to the emission hypothesis. 

M. Romanes performed several experiments upon 
bees which had the force of crucial tests of two 
opposed hypotheses, one, that bees possess a general 
sense of direction, irrespective of any special knowl- 
edge of their particular surroundings ; the other, 
that they are guided in their flight by a knowledge 
of the localities which they have been wont to fre- 
quent. M. Romanes took a score of bees in a box out 

1 Saigey, The Unity of Natural Phenomena, p. 66. 



HYPOTHESIS 201 

to sea, where there could be no landmarks to guide 
the insects home. None of them returned home. 
Then he liberated a second lot of bees on the sea- 
shore, and, none of these returning, he liberated 
another lot on the lawn between the shore and the 
house. None of these returned, although the dis- 
tance from the lawn to the hive was not more than 
two hundred yards. Lastly, he liberated bees in 
different parts of the flower-garden on either side 
of the house, and these at once returned to the 
hive; and with repetition of the experiment, a 
similar result, even arriving at the hive before 
he himself had time to run from the place where 
he had liberated them to the hive. As the garden 
was a large one, many of them had to fly a greater 
distance, in order to reach the hive, than those 
liberated on the front lawn. Their uniform suc- 
cess, therefore, in finding their way home so im- 
mediately was no doubt due to their special 
knowledge of the flower-garden, and not to any 
general sense of direction. 1 

The hypothesis that leads to verification by ex- 
periment represents true scientific procedure, and 
that which has actually been the most effective 
instrument of research in all the various spheres of 
human investigation. The old controversy between 
Mill and Whewell admits of a ready adjustment in 
this regard. Whewell emphasized discovery as the 
heart of the system of induction, leading to the 
framing of hypotheses whose chief test was not 

1 Lubbock, On the Senses, Instincts, and Intelligence of 
Animals, pp. 2G9, 270. 



202 INDUCTIVE LOGIC 

experimental so much as the capability of account- 
ing for the given phenomena. Mill, on the other 
hand, insisted that logic was essentially proof, and 
not discovery. He, accordingly, emphasized the 
experimental testing by means of his several meth- 
ods, as being the all-important part of the in- 
ductive method. He had little concern for the 
origin of the suggestions as to the most likely 
causal elements in the midst of a complex phe- 
nomenon. The primary function of logic, according 
to him, is merely to prove or disprove. The ideas 
of Whewell and Mill are not necessarily contradic- 
tory; they can be regarded as mutually supple- 
mentary, which gives us a true account of the ideal 
logical method, where hypothesis suggests the line 
of experiment, and experiment in turn confirms 
hypothesis. In such a method, as can be seen in 
the illustration given, there is a blending of deduc- 
tive and inductive reasoning, which is the general 
characteristic of all actual processes of thought. 
As Sigwart has so admirably put it: "Without 
quickness of combination, by which we can call up 
a number of possible analogies and apply them to 
the unexplained case; without a happy power of 
divination which is guided by unanalyzable associa- 
tions to discover that analogy which embraces most 
aspects of the event; finally, without imagination 
to construct connections for which the only ground 
may be a hidden similarity, our thoughts, if com- 
pelled to proceed strictly according to method, would 
frequently be condemned, by the impossibility of 
discovering in this way a sufficiently grounded con- 



HYPOTHESIS 203 

nection, to complete stagnation. But the fact is in 
no way contrary to the nature of induction ; it is a 
necessary consequence of it. We cannot even begin 
the process of inference without making general 
assumptions ; and the general proposition which we 
get by summing up a number of instances is really 
a hypothesis, to which, it is true, we are led clearly 
and certainly in this case. But between these most 
general presuppositions, upon which all induction 
is grounded, and the simplest cases to which they 
can be applied, there is a wide region within which 
the hypotheses which are always necessary for in- 
duction can only be formed tentatively, in order to 
give some definite direction to investigation, to serve 
in our analysis of phenomena into their elements as 
a means of breaking up complete phenomena on cer- 
tain lines, and to invent the experiments which will 
make it possible to confirm or refute an opinion." 1 

i Sigwart, Logic, Vol. II. p. 423. 



CHAPTER XIV 
Analogy 

It often happens that the cause of a phenomenon 
is disclosed by the fact that the cause of a similar 
phenomenon is known, and the inference then fol- 
lows that the similar phenomena have similar 
causes. Such a process of inference is determina- 
tion by analogy. Analogy, considered in its rela- 
tion to the inductive processes, occupies a twofold 
position. In the first place, when a complex phe- 
nomenon is given, as preliminary to the formation 
of any hypothesis, as to the probable cause which 
will, in turn, lead to experimental determination 
by one of the inductive methods, the mind instinc- 
tively examines, with sweeping glance, every detail 
of the phenomenon for the purpose of discovering 
some familiar features that may prove suggestive 
of known relations and functions occurring in other 
spheres. Analogical suggestion, therefore, initiates 
every inductive inquiry. 

In the second place, in every inductive general- 
ization there is an extension of the known into 
unknown regions, by virtue of the principle of 
analogy expressed in what we may style its limit- 
ing case. For instance, when we have examined 
204 



ANALOGY 205 

a number of A f s and find them always character- 
ized by the mark B, and then by generalization 
rise to the proposition, All A's are B, we do so by 
reason of postulating an analogy between all the 
individual A's of so strictly an accurate nature, that 
it amounts to essential identity. I have therefore 
called this the limiting case of analogy ; and this 
resemblance of particulars is the ground of all uni- 
versals whereby they manifest an identity in the 
midst of differences. AVe are therefore justified in 
affirming that all inductive generalizations present 
an aspect of analogical inference. 

Analogy, considered as a mental process, is 
grounded in the law of similarity. This tendency 
of noting resemblance makes possible the extension 
of knowledge. The formation of our concepts is, 
in the main, an analogical procedure; just as the 
generalization of an universal depends upon our 
discrimination of the elements which are similar 
from those which are different. While analogy 
thus functions in all the logical processes of 
thought, it is used in a more restricted sense to 
indicate that mode of inference especially which 
proceeds from a number of observed characteristics 
that are similar, to others which are thereby judged 
to be similar also. This -method is very potent as 
an instrument of discovery. In 1845, Faraday dis- 
covered the magnetic rotary polarization of light ; 
by analogical reasoning, AVaitmann in the following 
year inferred that a similar result would be attained 
with a beam of heat, which was afterwards experi- 
mentally verified. The so-called "natural kinds" 



206 INDUCTIVE LOGIC 

furnish manifold illustrations of conclusive analo- 
gies. They possess numerous properties, some of 
them known and others unknown. Through large 
groups of them are found similar characteristics 
side by side with manifest differences, and yet the 
similarities are so striking that often, when new 
properties are discovered in certain members of the 
group, there seems to be ground for inferring their 
existence in other members of the group also. 
Certain properties known to exist in potassium and 
sodium were inferred to be present in rubidium and 
csesium ; the carbonates of sodium and potassium 
are not decomposed by a red heat, and it was in- 
ferred that the same would prove true of the car- 
bonates of rubidium and csesium ; and such proved 
to be the case. Some of the statements which are 
true of chlorine are found to be true of bromine 
and iodine. Mr. Gore, having found the molecu- 
lar change in antimony electro-deposited from its 
chloride, he inferred and discovered the same in 
that deposited from its bromide and iodide. Sir 
Humphry Davy, having discovered that potassium 
might be isolated by means of electrolysis, imme- 
diately inferred and proceeded to prove by experi- 
ment that it would be possible also to isolate sodium 
and other substances of analogous properties. 1 

The principle of analogy lies at the basis of all 
classification, the separating and grouping together 
in appropriate divisions individuals which possess 
certain salient attributes in common. 

Professor Jevons' definition of classification em- 

1 Gore, The Art of Scientific Discovei*y, p. 522. 



ANALOGY 207 

bodies at the same time a full statement of its 
exact logical significance as an instrument of re- 
search, and therefore I give it in full : " By the 
classification of any series of objects, is meant 
the actual or ideal arrangement together of those 
which are alike and the separation of those which 
are unlike, the purpose of this arrangement being, 
primarily, to disclose the correlations or laws of 
union of properties and circumstances, and secon- 
darily, to facilitate the operations of the mind in 
clearly conceiving and retaining in the memory the 
characters of the object in question." 1 In describ- 
ing the purpose of classification, the latter clause 
is more a psychological desideratum than logical ; 
the former specification contains its logical pur- 
pose; namely, to disclose the correlations or laws 
of union of properties and circumstances. This 
may be illustrated in the grouping together of 
potassium, sodium, caesium, rubidium, and lithium, 
and calling them the alkaline metals. This was 
done by virtue of the common characteristics in 
the midst of their individual peculiarities ; namely, 
they all combine very energetically with oxygen 
to decompose water at all temperatures, and form 
strongly basic oxides, which are highly soluble in 
water, yielding powerful caustic and alkaline hy- 
drates from which water cannot be expelled by 
heat; their carbonates are also soluble in water, 
and each metal forms only one chloride. The 
manifest advantage of classifying these metals 
together lies in its suggestive capacity, as we have 

1 Jevons, Principles of Science, p. 677. 



208 INDUCTIVE LOGIC 

already noted in illustrations above given. So 
many observed similarities suggest inferences by 
analogy ; when, for instance, a new property is 
discovered in any one or two of the metals of this 
class, the idea immediately suggests itself that the 
same property may possibly extend over all the 
metals of the same class. Not only is such an idea 
suggested, but along with it there exists an ante- 
cedent probability respecting its solution in accord- 
ance with the suggestion which analogy starts. 

An excellent illustration of the practical results 
attained through a scientific use of classification is 
found in Mr. Lockyer's researches on the sun. 1 As 
a guide as to what elements to look for in the sun's 
photosphere, he prepared a classification of elements 
according as they had or had not been traced in 
the sun, together with a detailed statement of the 
chemical nature of each element. He was then 
able to observe that the elements found in the sun 
were, for the most part, those forming stable com- 
pounds with oxygen. He then inferred that the 
other elements which were known to form stable 
compounds with oxygen would, in all probability, 
be found present in the sun. Starting upon this 
suggested track, he succeeded in discovering five 
such metals. 

Analogical inference carries special weight when 
it is based upon the principle of teleology; that 
is, when any observed phenomena seem to possess 
structural contrivances adapted to ends, in some 
degree, at least, similar to human contrivances 
1 Quoted by Jevons in Principles of Science, p. 676. 



ANALOGY 209 

designed to produce certain proposed ends. When 
this similarity is apparent, it suggests the possi- 
bility that an observed contrivance in nature may 
subserve ends beyond the possibility of observa- 
tion, and which, therefore, may be inferred really 
to exist. We have seen that the ground of all 
inference lies in the representation of any given 
phenomena of consciousness as cohering in one 
system, which comprehends the several parts in 
a common unity of such a nature that, knowing 
some of the parts and their relations, we infer the 
character and function of other parts not known, 
and yet which that already known necessitates. 
And among the many kinds of relation that may 
obtain between part and part, or part and whole, 
the teleological is a very common one, and, more- 
over, by its nature necessitates certain consequences 
that lie beyond the sphere of observation, and yet, 
nevertheless, may very properly be supplied by in- 
ference. In other words, the causal connections in 
a system are not merely those of an efficient or 
a formal cause; they may, with a like force and 
suggestiveness, be considered in the light of a final 
cause; that is, the presence of means adapted to 
certain ends, or of organs adapted to certain neces- 
sary functions, or of contrivances of a mechanical 
nature as though designed for a specific purpose. 

Janet has specially emphasized the importance 
and prevalence of this kind of inference, and, as an 
illustration of the cogency of inference based upon 
finality, he urges that the certitude which the belief 
in the intelligence of our fellow-men gives us is 
p 



210 INDUCTIVE LOGIC - 

based upon analogical reasoning of this type ; and 
that, moreover, this belief, resting upon such a basis, 
is one of the strongest beliefs which we possess. 
He says: "Now, if we ask ourselves why we 
suppose that other men think, we shall see that it 
is in virtue of the principle of final causes. In 
effect, what is it that experience shows in the 
actions of other men, but a certain number of 
phenomena co-ordinated in a certain manner, and 
bound not only together, but also to a future phe- 
nomenon more or less remote ? Thus when we see 
a man prepare his food by means of fire, we know 
that this assemblage of phenomena is connected 
with the act of taking food ; when we see a painter 
drawing lines on a canvas, we know that these 
apparently arbitrary acts are connected with the 
execution of a picture ; when we see a deaf mute 
making signs which we do not understand, we be- 
lieve that these gestures are connected with a final 
effect, which is to be understood by him to whom 
he makes them ; in fine, when men speak, we see 
that the articulations of which a phrase is com- 
posed are co-ordinated to each other so as to pro- 
duce a certain final effect, which is to awaken in us 
a certain thought and sentiment. Now we cannot 
see such co-ordinations, whether actual or future, 
without supposing a certain cause for them ; and 
as we know by internal experience that with our- 
selves such co-ordinations only take place under 
the condition that the final effect is previously 
represented in our consciousness, we suppose the 
same thing in the case of other men; in a word, 



ANALOGY 211 

we suppose for them the consciousness of an end, 
a consciousness reflecting more or less, according 
as the circumstances more or less resemble those 
that accompany in ourselves the reflecting con- 
sciousness. Thus when we affirm the intelligence 
of other men, we affirm a truth of indisputable cer- 
titude ; and yet we only affirm it on the ground of 
analogy, and of analogy guided by the principle of 
final causes." 1 

In this illustration of Janet's we have the idea 
of a system of co-ordinated parts especially promi- 
nent; and for a satisfactory account of the rela- 
tions obtaining in such a system, it will be seen 
how indispensable it is to postulate the theory of 
final cause. This mode of inference finds a striking 
illustration in the famous discovery of Harvey, con- 
cerning the circulation of the blood. In the early 
part of the seventeenth century, while Harvey was 
his pupil, the celebrated anatomist, Fabricius Aqua- 
pendente of Padua, observed that many veins con- 
tain valves which lie open as long as the blood is 
flowing towards the heart. Harvey, learning of 
this fact, saw in it the suggestion of an adaptation 
of means to an end ; namely, a contrivance so fash- 
ioned by nature as to permit the blood to flow 
always in one direction . only, and to prevent its 
flow in an opposite direction. Observation of other 
portions of the circulatory mechanism led to a con- 
firmation of the idea, and to the discovery of the 
circulation of the blood. 2 

1 Janet, Final Causes, pp. 113, 114. 

2 Gore, Art of Scientific Discovery, p. 571. 



212 INDUCTIVE LOGIC 

Again, many flint substances have been discov- 
ered, as though curiously wrought, with sharp 
edges and a place as though designed for a handle, 
with which to wield the stone as a weapon or a 
tool ; it has been inferred from these general char- 
acteristics that the stones were so constructed by 
human effort, and used by human beings for the 
purposes for which they evidently seem to be 
adapted. This inference is based upon an analogy 
between the peculiar shapes of such stones, and 
known shapes designed and used by man. 

This form of analogy has proved specially sug 
gestive in researches regarding plant and animal life. 
Sir John Lubbock gives the following description of 
the common white dead-nettle, with the explanation 
of its functions that is evidently a teleological in- 
ference : " The flower consists of a narrow tube, 
somewhat expanded at the upper end, where the 
lower lobe of the corolla forms a platform, on each 
side of which is a small projecting lobe. The upper 
portion of the corolla is an arched hood, under 
which lie four anthers in pairs, while between them 
and projecting somewhat downwards is the pointed 
pistil. At the lower end, the tube contains honey, 
and above the honey is a row of hairs almost clos- 
ing the tube. Now, why has the flower this pecul- 
iar form ? What regulates the length of the tube? 
What is the use of this arch ? What lessons do 
these lobes teach us ? What advantage is the 
honey to the flower ? Of what use is the fringe of 
hairs ? Why does the stigma project beyond the 
anthers ? Why is the corolla white, while the rest 



ANALOGY 213 

of the plant is green ? Similar questions may of 
course be asked with reference to other flowers. 
At the close of the last century, Conrad Sprengel 
published a valuable work, in which he pointed out 
that the forms and colors, the scent, honey, and 
general structure of flowers, have reference to the 
visits of insects, which are of importance in trans- 
ferring the pollen from the stamens to the pistil. 
Mr. Darwin developed this theory and proved ex- 
perimentally that the special service which insects 
perform to flowers, consists not only in transferring 
the pollen from the stamens to the pistil, but in 
transferring it from the stamens of one flower to 
the pistil of another." 1 The line of subsequent ob- 
servation and experiment was thus originally sug- 
gested by the structural appearance of these flowers 
which seemed formed for some specific end. The 
questions, once started, — To what end ? To what 
purpose ? For what use ? — led to the theory of 
Sprengel and the corroborative experiments of 
Darwin. 

This is further illustrated in some very inter- 
esting flower structures, also described by Sir 
John Lubbock, which indicate peculiar contrivances 
for the destruction of insects. The peculiarity of 
formation first suggested some such end as this, 
which has since been proved by careful observation 
to be the case. "The first observation on insect- 
eating flowers was made about the year 1868 by 
Ellis. He observed that in Dionsea, a North 
American plant, the leaves have a joint in the 

1 Lubbock, Scientific Lectures, pp. 1, 2. 



214 INDUCTIVE LOGIC 

middle, and thus close over, kill, and actually di- 
gest any insect which may alight on them. An- 
other case is that of Utricularia, an aquatic species 
which bears a number of utricles or sacs, which 
have been supposed to act as floats. Branches, 
however, which bear no bladders float just as well 
as the others, and there seems no doubt that their 
real use is to capture small aquatic animals, which 
they do in considerable numbers. The bladders, in 
fact, are on the principle of an eel-trap, having an 
entrance closed with a flap, which permits an easy 
entrance, but effectually prevents the unfortunate 
victim from getting out again. In the genus, Sar- 
racenia, some of the leaves are in the form of a 
pitcher. They secrete a fluid, and are lined inter- 
nally with hairs pointing downwards. Up the out- 
side of the pitcher there is a line of honey glands 
which lure the insects to their destruction. Flies 
and other insects which fall into this pitcher cannot 
get out again and are actually digested by the plant." 1 
In the example where the idea of an eel-trap sug- 
gested the possible function of the similar struct- 
ure in the plant, Utricularia, we find one of the 
most striking illustrations of this mode of ana- 
logical inference. It was an easy and natural 
transition from similarity of structure to similarity 
of function. To give an idea of the great number 
of teleological phenomena in the vegetable and 
animal world, and the wealth of possible sugges- 
tion stored away in these various structures, and 
disclosed by a sagacious analysis, I quote a remark 

1 Lubbock, Scientific Lectures, pp. 4, 5. 



ANALOGY 215 

of Sir John Lubbock's in commenting upon the 
variation of color and markings of caterpillars : " I 
should produce an impression very different from 
that which I wish to convey, were I to lead you to 
suppose that all these varieties have been explained 
or are understood. Far from it ; they still offer a 
large field for study ; nevertheless, I venture to 
think the evidence now brought forward, however 
imperfectly, is at least sufficient to justify the con- 
clusion that there is not a hair or a line, not a spot 
or a color, for which there is not a reason, — which 
has not a purpose or a meaning in the economy of 
nature." * 

An illustration given by Darwin shows this mode 
of inference applied to the sphere of animal life 
also. He says : " The great size of the bones of 
the megatherioid animals was a complete puzzle to 
naturalists until Professor Owen lately solved the 
problem with remarkable ingenuity. The teeth 
indicate, by their simple structure, that these mega- 
therioid animals lived on vegetable food, and prob- 
ably on the leaves and small twigs of trees ; their 
ponderous forms and great, strong, curved claws 
seem so little adapted for locomotion that some emi- 
nent naturalists have actually believed that, like 
the sloths, to which they are intimately related, 
they subsisted by climbing back downwards on 
trees, and feeding on the leaves. It was a bold, 
not to say preposterous, idea, to conceive even ante- 
diluvian trees with branches strong enough to bear 
animals as large as elephants. Professor Owen, 
1 Lubbock, Scientific Lectures, pp. 66, 67. 



216 INDUCTIVE LOGIC 

with, far more probability, believes that, instead of 
climbing on the trees, they pulled the branches 
down to them, and tore up the smaller ones by 
the roots, and so fed on the leaves. The colossal 
breadth and weight of their hinder quarters, which 
can hardly be imagined without having been seen, 
become, on this view, of obvious service, instead of 
being an encumbrance: their apparent clumsiness 
disappears. With their great tails and their huge 
heels firmly fixed like a tripod on the ground, they 
could freely exert the full force of their most 
powerful arms and great claws. Strongly rooted, 
indeed, must have been that tree which could have 
resisted such force ! The Mylodon, moreover, was 
furnished with a long extensile tongue like that of the 
giraffe, which, by one of those beautiful provisions 
of nature, thus reaches, with the aid of its long neck, 
its leafy food." 1 Throughout we observe analogical 
inference based upon these teleological marks, and 
furnishing a basis for a satisfactory hypothesis. 

We see what a wide field thus opens in the 
region of biology alone for the discovery of resem- 
blances leading to the appreciation of the fuller 
teleological significance of plant and animal life. 

In the illustrations given, both of the teleologi- 
cal and other forms of analogy, we notice that its 
chief logical function is that of suggestion of some 
hypothesis which may or may not be afterwards 
confirmed by subsequent experiment. Some of the 
most important discoveries of science have arisen 
from analogical suggestions. Sir John Herschel 

1 Darwin, Voyage of a Naturalist, pp. 106, 107. 



ANALOGY 217 

was led by observed analogies to predict certain 
phenomena afterwards verified experimentally by 
Faraday. Herschel had noticed that a screw-like 
form, known as helicoidal dissymmetry, was ob- 
served in three cases, namely, in electrical helices, 
plagihedral quartz crystals (that is, crystals having 
an oblique spiral arrangement of planes), and the 
rotation of the plane of polarization of light. As 
Herschel himself said : " I reasoned thus : Here 
are three phenomena agreeing in a very strange 
peculiarity. Probably this peculiarity is a connect- 
ing link, physically speaking, among them. Now, 
in the case of the crystals and the light, this prob- 
ability has been turned into certainty by my own 
experiments. Therefore, induction led me to con- 
clude that a similar connection exists, and must 
turn up, somehow or other, between the electric 
current and polarized light, and that the plane of 
polarization would be deflected by magneto-elec- 
tricity." Herschel thus anticipated Faraday's ex- 
perimental discovery of the influence of magnetic 
strain upon polarized light. 1 

Another important discovery — the germ-theory 
of epidemic disease — was first suggested by an 
analogy. In the theory, as expressed by Kircher, 
and favored by Linnaeus, and afterwards supported 
by Sir Henry Holland, its special strength, accord- 
ing to Professor Tyndall, " consisted in the perfect 
parallelism of the phenomena of contagious disease 
with those of life. As a planted acorn gives birth 
to an oak competent to produce a whole crop of 

1 Jevons, Principles of Science, p. 030. 



218 INDUCTIVE LOGIC 

acorns, each gifted with the power of reproducing the 
parent tree, and as thus from a single seedling a 
whole forest may spring, so, it is contended, these 
epidemic diseases literally plant their seeds, grow 
and shake abroad new germs, which, meeting in the 
human body their proper food and temperature, 
finally take possession of whole populations." 1 

The theory of evolution was first suggested to 
Mr. Darwin by the analogous phenomena observed 
in artificial selection and breeding. The transition 
to natural selection was easily made, especially as, 
on reading Malthus, On Population, he conceived 
the idea of a struggle for existence as the inevitable 
result of the rapid increase of organic beings. This 
idea necessitated the natural selection, which he 
needed to account for results similar to the artifi- 
cial selection, and thus his theory grew out of an 
analogy as its beginning. Moreover, in the devel- 
opment of the theory in its manifold details, other 
analogies proved also suggestive. For instance, 
there is the supposed analogy between the growth 
of a species and the growth of an individual. 
It supposes, for example, as Professor Clifford has 
put it, "that the race of crabs has gone through 
much the same sort of changes as every crab goes 
through now, in the course of its formation in the 
egg, — changes represented by its pristine shape 
utterly unlike what it afterwards attains, and by 
its gradual metamorphosis and formation of shell 
and claws." 2 

1 Tyndall, Fragments of Science, p. 287. 

2 Clifford, Lectures and Essays, p. 86. 



ANALOGY 219 

The germ-theory of putrefaction, first suggested 
by Schwann, received confirmation through certain 
resemblances noted by Professor Lister between 
fermentation and putrefaction. In his Introduc- 
tory Lecture before the University of Edinburgh, 
Professor Lister called attention to the fact that 
fermentation and putrefaction present a very 
striking parallel. In each a stable compound — 
sugar in one case, albumen in the other — under- 
goes extraordinary chemical changes under the 
influence of an excessively minute quantity of a 
substance which, regarded chemically, would be 
considered inert. It was pointed out, also, by Pro- 
fessor Lister, in this connection, that, as was well 
known, one of the chief peculiarities of living or- 
ganisms, is that they possess extraordinary powers 
of effecting chemical changes in materials in their 
vicinity out of all proportion to their energy as 
mere chemical compounds. Such being the facts 
in the case, and, moreover, the fermentation of 
sugar being generally allowed to be occasioned by 
the presence of living organisms, Professor Lister's 
inference was that putrefaction was due to an 
analogous agency. 1 

A discovery in quite a different sphere, that of 
mathematics, leading to the branch of analytical 
geometry, was first suggested to Descartes through 
observing the resemblances existing between geom- 
etry and algebra. In a similar manner, Boole was 
led by the resemblances noted between algebra 
and logic, to give expression to the same in a sys- 
1 Tyndall, Fragments of Science, pp. 300-302. 



220 INDUCTIVE LOGIC 

tern which he called the laws of thought, and which 
has become the basis of a general or symbolic logic. 

While there are thus unquestionable evidences of 
the value of analogy as a form of inference, there 
are also cases of false analogy unfortunately so nu- 
merous as to discredit the process wholly in some 
quarters. It will be well, therefore, to indicate 
some of the requirements of true analogy : — 

1. In the first place the resemblance must be a 
preponderating one ; that is, the phenomena com- 
pared must show a more striking agreement than 
difference. Some writers have balanced agreement 
against difference upon a purely numerical basis of 
comparison, forming what may be called an analogi- 
cal ratio, with points of similarity forming the numer- 
ator, and the points both of similarity and difference, 
plus the unknown, that is, the total number, form- 
ing the denominator. Such a representation of the 
force of an analogy is given by Mill, Bain, and 
others. I think, however, that this representation 
is apt to be misleading in producing the impression 
that the mere number of points of agreement, irre- 
spective of their significance, is the chief feature of 
analogy. Whereas it is the weight of the agreeing 
attributes, and not the number, that counts. As has 
been before said, in analogy we weigh instances, 
and do not count them. The analogical ratio ex- 
pressed numerically, as above, is really equivalent 
to the ratio of probability which will be described in 
the following chapter. I have therefore changed 
the usual wording of this requirement, so that it 
reads, the resemblances must be more striking than 



ANALOGY 221 

the differences. This provides for cases when per- 
haps a few points of resemblance will be of such a 
nature as to outweigh many points of difference in 
the total estimate. 

This requirement also excludes all fanciful anal- 
ogies and all resemblances resting upon a figurative 
rather than a real basis. For instance, the advo- 
cates of annual Parliaments in the time of the 
Commonwealth, urged their case on the analogical 
ground that a body politic is similar to a living body 
and that serpents annually cast their skin, which, 
being no doubt for a beneficial purpose, might well 
be imitated. 

2. In noting the points of resemblance between 
two phenomena, all circumstances which are known 
to be effects of one cause must therefore be re- 
garded not as many, but as one. For instance, two 
chemical oxides may be compared; the effects com- 
mon to each may be due to the presence of the 
oxygen which each contains and therefore must not 
be regarded in the light of independent marks of 
similarity. 

3. If we infer by analogy that a substance pos- 
sesses a certain property which we know is incom- 
patible with some one or other known properties 
of the substance, the analogy is at once discredited. 
We may infer that the moon is inhabited, by virtue 
of the many points of resemblance between the 
moon and the earth. However, the fact that the 
moon has no atmosphere necessary to sustain life, 
at once makes such an argument based upon an- 
alogy wholly out of the question. 



222 INDUCTIVE LOGIC 

4. There are certain special requirements refer- 
ring to that particular form of analogy which is 
based upon teleological considerations. They are 
as follows : — 

a. This principle must never be used as an argu- 
ment against an observed fact, or an established 
law of nature. While this precaution is not neces- 
sary at the present "time, in scientific circles at 
least, still there was a time when its counsel was 
sorely needed. When in astronomy it was proved 
that there Were suns gravitating around other suns, 
without our solar system, this was objected to upon 
the following ground, as given by one Nicholas 
Puss, a celebrated astronomer, at the end of the 
eighteenth century : " What is the good of some 
luminous bodies revolving round others ? The sun 
is the only source whence the planets derive light 
and heat. Were their entire systems of suns con- 
trolled by other suns, their neighborhood and their 
motions would be objectless, their rays useless. The 
suns have no need to borrow from strange bodies 
what they themselves have received as their own. 
If the secondary stars are luminous bodies, what is 
the end of their motives ? " 

There is, moreover, another abuse of the principle 
of final causes, which has also historic interest 
rather than any present pertinence ; namely, oppos- 
ing certain false teleological ideas to established 
discoveries or inventions, with a mistaken zeal, in 
defence of a Divine Providence. For instance, at 
the time of Jenner's great discovery, an English 
physician, Dr. Rowley, said of small-pox : " It is a 



ANALOGY 223 

malady imposed by the decree of heaven, and vac- 
cination is an audacious and sacrilegious violation 
of our holy religion. The designs of these vaccina- 
tors appear to defy heaven itself, and the very will 
of God." The introduction of winnowing machines 
into Scotland met with bitter opposition on the 
ground that the winds were the work of God, and 
that the wind thus artificially raised was a veritable 
"devil's wind," as they were wont to call it. Sir 
Walter Scott, in Old Mortality, has the old Mause 
say to her mistress : " Your ladyship and the stew- 
ard are wishing Cuddie to use a new machine to 
winnow the corn. This machine opposes the de- 
signs of Providence, by furnishing wind for your 
special use, and by human means, in place of asking 
it by prayer, and waiting with patience till Prov- 
idence itself sends it." 

b. Final causes should never be employed to 
explain phenomena which do not exist. As M. 
Florens has said : " We must proceed not from final 
causes to facts, but from facts to final causes ; that 
is, we should not superimpose final causes upon 
phenomena. We must see them in phenomena 
themselves, and we must not arbitrarily project a 
teleological idea, purely subjective, upon an objec- 
tive ground. Thus in ancient times, Hippocrates 
is said to ' have admired the skill with which the 
auricles of the heart have been made to blow the 
air into the heart.' " 

c. We must distinguish accidental from essential 
marks of finality, and not be led into fanciful or 
far-fetched analogies. Voltaire has expressed such 



224 INDUCTIVE LOGIC 

a defect when in satire he made that famous re- 
mark, "Noses are made in order to bear spectacles." 

Bernardin de Saint-Pierre says: "Dogs are usu- 
ally of two opposite colors, the one light, the other 
dark, in order that whenever they may be in the 
house, they may be distinguished from the furni- 
ture, with the color of which they might be con- 
founded. . . . Wherever fleas are they jump on 
white colors. This instinct has been given them, 
that we may the more easily catch them." And 
again the same writer says : " The melon has been 
divided into sections by nature, for family eating." x 
All such grotesque inferences will give an idea of 
how readily the imagination will run riot if allowed 
to remain uncurbed by the reason. 

5. Analogy should never be regarded as having 
more weight than that of extremely high probabil- 
ity, even in cases seemingly most conclusive. Its 
true function is suggestive, leading to hypothesis 
and experiment, and it needs this supplementary 
proof. It was an inference based on analogy, for 
instance, which suggested the probability that the 
Binomial Law, having proved to be valid as regards 
the second, third, and fourth powers, might also be 
extended to the fifth, and so on to the other powers 
indefinitely. This suggestion offered no real basis, 
however, upon which the Binomial Theorem could 
rest ; it needed mathematical demonstration to con- 
firm and generalize its expression in the special 
cases already experimentally tested, so as to cover 

1 The illustrations upon the abuse of final causes I have taken 
from Janet's admirable chapter, — Chapter VIII. of Appendix. 



ANALOGY 225 

all possible exponents, both positive and negative, 
fractional and integral. 

So also the discovery of the circulation of the 
blood was first suggested to Harvey, as has been 
said, by analogical considerations upon observed 
teleological phenomena. Harvey, however, was not 
content with this suggestion merely. He was led 
to experiment upon the veins and arteries ; he tied 
an artery and vein, and carefully observed the me- 
chanical effects upon the two sides of the tied parts. 
Experiments of this nature, with close observation 
and study, were kept up most diligently, and with 
rare perseverance, for nineteen years, before he had 
traced the entire course of the blood through all 
parts of the human body, and, in a manner wholly 
satisfactory to himself, verified the first statement 
of this theory. 



CHAPTER XV 

Probability 

There are certain phenomena of such a nature 
that their antecedents, being extremely complex, 
cannot be adequately comprehended by observation, 
however searching it may be ; nor can they be sub- 
jected to any analysis that will disclose the causal 
elements to which the effect in question is due. 
Moreover, with seemingly the same antecedents, 
the event sometimes happens, and sometimes does 
not ; and even with antecedents associated with an 
event as cause and effect respectively, nevertheless 
the event does not occur as we should naturally 
expect, while with antecedents associated with the 
contradiction of the event as cause and effect re- 
spectively, we find the occurrence of the event quite 
contrary to what we should naturally expect. The 
evidence of a constant connection between antece- 
dent and consequent, that we have found in so many 
cases which we have examined, is here wholly lack- 
ing. Regularity has been replaced by irregularity 
respecting such phenomena. For instance, I throw 
dice repeatedly ; the antecedent shaking of the 
box, and tossing the dice upon the table, is about 
the same each time, at least the difference can- 
226 



PROBABILITY 227 

not be determined, and yet the results vary with 
each successive throw. The causal determination 
in each case is so complex as to be beyond com- 
putation ; the initial position of the dice, the force 
of their ejection from the box, the height of the 
box above the table when they leave it, the ine- 
qualities of the table itself, a variation between 
the physical and geometrical centres of gravity 
of the dice, etc., all these make the antecedent 
so complex that a slight variation in any one of 
these conditions will affect the result. We find, 
therefore, double sixes at one time, a three and 
four at another, and so on indefinitely. 

Or, again, it sometimes happens that with perfect 
sanitary conditions a contagious disease will appear, 
that has always been regarded, and that correctly, as 
due to imperfect sanitation ; or, an entire disregard 
of sanitary requirements and of all the laws of 
health may yet give rise to no disease of special 
moment. Certain conditions of temperature, at- 
mospheric pressure, velocity and direction of the 
wind, may one day bring storm and rain, and as 
far as observation can detect, similar conditions 
may again bring fair weather. So, also, the rise 
and fall in stock and money markets is extremely 
susceptible to the varying conditions of indefi- 
nitely complex forces wholly beyond all powers 
of determination or of prediction. Such phe- 
nomena present a problem which the methods of 
inductive inquiry cannot deal with. Observation 
is not far-reaching enough to provide the data for 
the solution of the problem, and, even if it were, 



228 INDUCTIVE LOGIC 

our methods of computation and determination 
are not sufficiently adequate to solve problems of 
so many terms and of so complex a nature. 

The experimental methods are designed to test 
causes suggested by analogy, or a mental analysis ; 
but in such phenomena as these, the problem is 
not simply to find a causal connection. The causal 
connection may be established beyond all reasona- 
ble doubt, and yet the cause obtains in the midst 
of so complex a setting that the problem is really 
this, — to determine whether a cause, whose exact 
nature may be known or unknown, will prove 
operative or inoperative. The cause may be al- 
ways present and even its exact nature may be 
known, and yet the complex circumstances at- 
tending it may be of such a character that one 
alone, or two or more combining, may neutralize 
the operation of the cause, and on the other hand 
a slight variation of the combined circumstances 
may promote and even accelerate the operation of 
the cause in question. The problem then is to 
determine how often the event happens, and how 
often it fails of happening, the complex and in- 
determinate antecedent being present in all the 
instances examined. 

When we begin to count instances, we are re- 
minded that we must be in the near neighborhood 
of the sphere of enumerative induction. Enumera- 
tive induction, it will be remembered, treats in- 
stances by noting the number of observed coincident 
happenings of the antecedent and consequent under 
investigation, no attempt being made to analyze 



PROBABILITY 229 

their respective contents, or to determine a causal 
connection more definitely by means of any one or 
more of the inductive methods of research and veri- 
fication. The result of such an investigation may 
be formulated in a proposition of the form, Every 
A is B. This, strictly interpreted, has the force of, 
Every A that has been observed is B. The enu- 
meration of the kind of instances which we are dis- 
cussing in this chapter, however, differs from this 
in that the observation leads to a twofold residt, 
— a set of instances in which it is observed that 
the A's are B's also, another set, however, in 
which the ^4's are not B's. These instances are 
of such a nature that the observed A is an ante- 
cedent so extremely complex that the element 
within it, which is a cause capable of producing 
B, may either be absent without producing an 
appreciable change in the general natiire of A, or, 
being present, may be neutralized by some other 
element of A itself. The result gives a basis for a 
probable inference only ; and the nature of that in- 
ference will depend upon the preponderance of the 
observed happening, or of the failure of the event 
under investigation. 

The probability attached to such an inference, 
however, is different from the probability which 
characterizes the nature of enumerative induction. 
In the latter, when the observation has been widely 
extended and no exceptions noted, it is usual to say 
the result expressed in the proposition, Every A is 
B, has the force of a high degree of probability. 
In the instances, however, whose investigation 



230 INDUCTIVE LOGIC 

shows the result that some A's are B's, and some 
not, and yet where the. former, for instance, far 
outnumber the latter cases, then it may be inferred 
that the A's which in future we may meet with 
will probably be B's ; and the degree of probability 
expressed in such a proposition is commensurate 
with the preponderance of the number of observed 
affirmative instances over the negative. Here the 
probability refers to the validity of an inference 
concerning certain particular instances, be they 
many or be they few, which lie beyond the sphere 
of our present knowledge ; in enumerative induc- 
tion, the probability is attached to the universality 
of the proposition affirmed as a result of observa- 
tion that has not so far detected an exception. In 
the former case, the question of the universality 
of the result is conclusively answered, and that in 
the negative ; there can be no universal proposition 
possible, as some instances give A and B together, 
others give A with the absence of B; and the 
question of probability that here arises, therefore, 
refers to individual cases not yet examined, as to 
whether they severally will more likely correspond 
to the set of affirmative, or to that of the negative 
instances already noted. 

The comparison of the number of happenings 
with that of the failures of an event affords a 
basis for three kinds of inference, all of them in 
the sphere of probability. 

1. We ffhd in such a comparison a basis for the 
calculation of the probability of a particular event 
happening, in case there is a repetition of the cir- 



PROBABILITY 231 

cumstances which, in former cases, have sometimes 
produced the event, and sometimes have failed to 
produce it. If, according to former observation, 
the event has happened, let us say, seven times, 
and failed three, the probability, expressed nu- 
merically, of its happening again is t 7 q. The rule 
is, to express the probability of an event, take as 
numerator the number of times which the event 
has been observed to occur, and as denominator 
the total number observed, both of happening and 
failure ; the fraction thus expressed will represent 
the probability of the event happening. The coun- 
ter-probability may be represented by the number 
of observed failures of the event divided by the 
total number of cases observed. The counter-prob- 
ability, plus the probability, evidently is equal to 
unity. If, therefore, the probability is unity, the 
counter-probability will equal zero; that is, the 
probability in that case has merged into certainty. 
Zero, therefore, represents absolute impossibility. 
All fractions between the limits zero and one rep- 
resent varying degrees of probability from impos- 
sibility at one extreme to certainty at the other. 

Not only may there be this inductive basis for 
the calculation of probability, arising from actually 
observed instances ; there may be also a deductive 
calculation of probability based upon the known 
structure or nature of the phenomena themselves 
in advance of any observation as to their actual 
behavior. For instance, we say the probability 
of a penny turning up heads is %. Knowing the 
form of the penny and that there are but two 



232 INDUCTIVE LOGIC 

possibilities, heads or tails, and there being no 
reason why one should more likely turn up than 
the other, we say there is one chance favorable to 
heads as over against the two chances which rep- 
resent the total number of possibilities under the 
existing circumstances. With a die, in the form 
of a perfect cube, we say there is one chance of 
its turning up the face marked 1, as over against 
the six chances represented by the six faces, the 
total number ; here the probability is ^. Thus the 
basis for the calculation of probability may be a 
theoretical as well as an empirical one. 

In the estimate of the probability of an event in 
the actual conduct of affairs, we seldom express 
that probability numerically. I would say that we 
express a degree of probability adverbially rather 
than numerically ; that is, we say an event is quite 
probable, or it is very probable, or it is extremely 
probable. The fact is that, as regards most phenom- 
ena, we do not keep an exact or even approximate 
memorandum of the number of happenings compared 
with that of the failures. We rather classify our 
observations in terms of more or less. For instance, 
certain circumstances we observe produce about as 
many failures as happenings of an event; other 
circumstances produce far more happenings than 
failures ; others far less, and so on. Consequently 
we receive certain psychological impressions of 
varying degrees of intensity according to the pre- 
ponderance of happening over failure, or vice versa; 
this impression becomes the basis for estimating 
the probability in question, and the degree of that 



PROBABILITY 233 

probability is commensurate with the intensity of 
the original psychological impression arising from 
concepts of more or of less. In such a sphere, how- 
ever, as that devoted to the interests of betting, 
gambling, pool-selling, book-making, etc., probabili- 
ties are estimated according to observations and 
theoretical considerations, whose conditions are ex- 
pressed numerically ; and the amount risked in 
each case is strictly estimated according to the 
exact ratio of probability to counter-probability 
under the existing circumstances. 

The estimation of probability in terms of a 
greater or less degree is, however, more usual, and 
applicable to the conduct of human life generally. 
It has special force and utility as a mode of infer- 
ence, when the observed instances so far outnumber 
the exceptions as to create an impression of such 
a high degree of probability as to approximate 
practical if not theoretical certainty. For instance, 
it has been noted over a wide field of observation, 
that a second attack of scarlet fever is extremely 
rare. Exceptions have occurred and, therefore, by 
enumerative induction it is impossible to general- 
ize the universal proposition that a second attack 
will never occur. It is, however, possible to assert 
with somewhat positive assurance that it is highly 
probable that a person will be exempt from a second 
attack. 

Or, you hear that a person, whose name is un- 
known to you, has met with an accident in the 
city of New York, resulting fatally. You are not 
alarmed, and perhaps the possibility does not even 



234 INDUCTIVE LOGIC 

suggest itself to you, that the unknown person may 
prove to be a member of your own family, or a 
friend who at the time is known to be in New 
York. The probability against such a suggestion 
is so large as to preclude even the thought of it. 
Suppose, however, the accident occurred at one of 
the suburban stations. Your knowledge that your 
friend rides on one of the suburban trains each day 
to and from town, may be the ground of some 
anxiety, because in this case the range of possibili- 
ties is materially narrowed. Suppose, moreover, 
that the station where the accident occurred is at 
the village where your friend resides, your anxiety 
receives an additional increment; and, again, sup- 
pose it is at the hour at which your friend ordi- 
narily reaches this station, there is then increased 
apprehension on his account. Thus, as further 
knowledge limits the number of total possible cases, 
the denominator of the probability fraction is contin- 
ually decreasing, and therefore the probability itself 
continually increases, until it has developed from a 
fraction of insignificant proportions to one which is 
suggestive of great anxiety and suspense. 

2. The comparison of failure and happening of 
events based upon observation, or theoretical con- 
siderations of structure and nature, leads also to 
inferences concerning large numbers of instances 
considered together. If a memorandum is kept of 
the number of times an event has happened, and 
the number of times it has failed, and the total 
number of instances examined be sufficiently great, 
then the resulting ratio of favorable instances to 



PROBABILITY 235 

the total number will be found approximately 
repeated, if a second set of an equal number of 
instances be likewise examined. There is a law of 
tendency whereby nature seems to repeat herself 
even when the attendant circumstances of an event 
are most complex, and beyond all powers of accu- 
rate determination. As the result of observations 
extending over thousands and thousands of in- 
stances, it is affirmed that about one-fourth of the 
children born in the world die before the age of six 
years, and about one-half before the age of sixteen. 
Take a group of ten children, the ratios would per- 
haps be deviated from very materially ; in a group 
of a hundred the deviation is apt to be less ; in a 
group of a thousand, still less ; and in a group of 
one hundred thousand, the ratios as above given 
would be substantially realized. The approxima- 
tion would be so near that the error would be insig- 
nificant as compared with total number of cases. 
The following law, therefore, expresses this ten- 
dency, — that while in a small number of instances 
there is irregularity in the observed ratio between 
the number of times a given event has happened 
and its failures, still in a large number of instances 
this ratio tends towards a constant limit. This is 
clearly seen in the pitching of a penny ; 10 throws 
might very possibly result in 7 heads and 3 tails ; 
in 100 throws, however, the ratio expressing the 
result as to heads and tails observed will be much 
nearer \ than in the former case ; while if 1000 or 
10,000 throws be observed, the result will approxi- 
mate the ratio i. The comparison of observed cases 



236 INDUCTIVE LOGIC 

with the number given by the calculation of the 
probabilities in question has been made by Quetelet, 
also by Jevons. Their results are most significant 
and interesting. Quetelet made 4096 drawings 
from an urn containing 20 black balls and 20 white. 
Theoretically, he should have drawn as many white 
as black balls, 2048 each ; the actual drawings re- 
sulted in 2066 white balls and 2030 black. Jevons 
made 20,480 throws of a penny; the theoretical 
result should have been 10,240 heads; the actual 
result was 10,353 heads. 

The tendency towards a constant ratio in aggre- 
gates containing a considerable number of instances 
is strikingly illustrated in the record of baptisms 
taken from an old parish register in England. The 
number of male baptisms registered to every 1000 
female ran as follows for the respective years from 
1821 to 1830 : 1048, 1047, 1047, 1041, 1049, 1046, 
1047, 1043, 1043, 1034. We see with what surprising 
accuracy the constant ratio was repeated substan- 
tially, year after year. This tendency to approximate 
a constant ratio is seen even in such indeterminate 
events as railroad accidents. Here the causes pro- 
ducing the accidents are so numerous, so diverse, so 
complex and extending over so large an area, as, 
for example, the whole of the United States, that 
we should think that the results would exhibit so 
many variations from any definite ratio as abso- 
lutely to elude all attempts at accurate determina- 
tion. The following figures, however, given by the 
Interstate Commerce Commission, indicate results 
wonderfully corresponding for year after year : — 



PROBABILITY 



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PROBABILITY 239 

An examination of these figures will disclose the 
fact that there is a striking approximation to an 
accurately proportionate distribution of the number 
of accidents, of the killed and of the injured, 
throughout these several years. It will be noticed, 
also, that the distribution among employes, passen- 
gers, other persons, etc., tends towards a regularity 
that is remarkable when we consider the extreme 
complexity of the circumstances that must combine 
to produce these results. A like regularity seems 
to pervade every department of life. The total 
number of crimes is approximately the same, year 
after year ; the annual death-rate, the apportion- 
ment of deaths, moreover, to the several diseases as 
their evident causes, the number of missent letters 
that reach the Dead-Letter Office at Washington 
each year, the annual number of suicides, of di- 
vorces, all these diverse events indicate a regularity, 
in the long run, as regards their numerical estimate. 

The results which are thus attained regarding ag- 
gregates cannot be stated as probable results. If a 
sufficiently large number of instances are taken, the 
result will be certain within a very small, and in 
many cases an insignificant margin. In estimating 
the probability of a single event, the question is 
whether it will happen or not happen, and the ele- 
ment of uncertainty is therefore prominent. In 
dealing with aggregates, however, no such element 
of uncertainty enters ; the question is not whether 
or not there will be certain results, the question 
concerns rather the degree of exactness with which 
the results will approximate a definite ratio. And 



240 INDUCTIVE LOGIC 

the law of tendency is, that the larger the number 
of instances, the greater will be the approximation 
to an accurate and definite result. 

This is especially illustrated in the numerous in- 
surance companies, whose business is conducted upon 
the basis of an approximately constant death-rate. 
For instance, the general procedure is somewhat as 
follows : Suppose 10,000 persons insure their lives at 
$1000 per individual, and the annual death-rate ob- 
served over a rude extent of territory, and including 
a very large number of instances, amounts to 200 
persons out of 10,000. The losses then to the in- 
surance company will amount annually to $200,000 
on such a basis. These losses, distributed among 
the 10,000 insuring in the company, would amount 
to $20 apiece. The company, therefore, has a 
numerical basis for calculating the amount which 
each person must pay in order to cover the annual 
losses, and provide an assured revenue for the com- 
pany. 

I have, of course, stated the problem in round 
numbers, merely to illustrate in general the princi- 
ple involved ; the actual calculation is more compli- 
cated, because, in each particular case, the age of the 
individual and the varying death-rates for different 
years must be taken into account. The substantial 
standing of the innumerable insurance companies 
in our country bears witness to the fact that these 
enterprises are based upon a practical certainty re- 
garding death-rates when applied to large aggre- 
gates. Chance is thus eliminated almost entirely; 
that which would be a serious risk as regards an in- 



PROBABILITY 241 

dividual is substantially void of all risk when large 
numbers are concerned. 

Moreover, statistics covering different classes are 
often most valuable in indicating tendencies opera- 
tive in the classes when compared one with another. 
According to M. Loua (Economiste Frangais, 1882, 
Vol. I. p. 179), the following are the figures of the 
annual mortality in Paris : — 

The rich and well-to-do classes, 156 out of every 10,000 

inhabitants. 
The poor, 285 out of every 10,000 inhabitants. 

So also, in England, the average duration of life 
among the wealthy classes is from 55 to 56 years ; 
for the working classes it falls to 28 years, or even 
lower. 1 Such comparisons are significant in indi- 
cating underlying forces in society that otherwise 
might be overlooked, or, at least, not adequately 
appreciated, and which a limited observation could 
not accurately reveal. Mr. Darwin, after observing 
and experimenting upon a very large number of 
plants, found the following figures respecting the 
relative productivity of cross and spontaneously 
self-fertilized flowers: As regards the number of 
seeds per pod yielded by cross and self-fertilized 
flowers, the ratio was 100 to 41 respectively ; the 
crossed seeds compared with an equal number of 
the spontaneously self-fertilized seeds were heavier, 
in the ratio of 100 to 88. 2 The ratios thus disclosed 
in examining a large number of instances could 
not have been gained by any experimental method 

1 Gide, Political Economy, p. 405. 

2 Darwin, Cross and Self Fertilization, p. 165. 



242 INDUCTIVE LOGIC 

adapted for dealing with individual instances. Al- 
though the cause is not quantitatively determined, 
a tendency of a constant nature towards a definite 
end is clearly indicated. 

Kace characteristics are often disclosed by com- 
parative statistics, and the presence or absence of 
moral causes especially are thus revealed which 
otherwise could not be determined with any con- 
siderable degree of definiteness. The following 
tables will indicate this : — 

Suicides. — In European cities the number of 
suicides per 100,000 inhabitants is as follows : 
Paris, 42; Lyons, 29; St. Petersburg, 7; Moscow, 
11 ; Berlin, 36 ; Vienna, 28 ; London, 23 ; Rome, 
8 ; Milan, 6 ; Madrid, 3 ; Genoa, 31 ; Brussels, 15 ; 
Amsterdam, 14 ; Lisbon, 2 ; Christiania, 25 ; Stock- 
holm, 27 ; Constantinople, 12 ; Geneva, 11 ; Dres- 
den, 51. Madrid and Lisbon show the lowest, 
Dresden the highest figure. 

The average annual suicide rate in countries of 
the world per 100,000 persons living is given by 
Barker as follows : Saxony, 31.1 ; Denmark, 25.8 ; 
Schleswig-Holstein, 24.0 ; Austria, 21.2 ; Switzer- 
land, 20.2 ; France, 15.7 ; German Empire, 14.3 ; 
Hanover, 14.0 ; Queensland, 13.5 ; Prussia, 13.3 ; 
Victoria, 11.5; New South Wales, 9.3; Bavaria, 9.1 ; 
New Zealand, 9.0; South Australia, 8.9; Sweden, 
8.1 ; Norway, 7.5 ; Belgium, 6.9 ; England and 
Wales, 6.9 ; Tasmania, 5.3 ; Hungary, 5.2 ; Scot- 
land, 4.0; Italy, 3.7; Netherlands, 3.6; United 
States, 3.5 ; Russia, 2.9 ; Ireland, 1.7 ; Spain, 1.4. 



PROBABILITY 243 

The causes of suicide in European countries are 
reported as follows : Of 100 suicides : Madness, de- 
lirium, 18 per cent ; alcoholism, 11 ; vice, crime, 19 ; 
different diseases, 2 ; moral sufferings, 6 ; family- 
matters, 4 ; poverty, want, 4 ; loss of intellect, 14 ; 
consequence of crimes, 3 ; unknown reasons, 19. 

Homicides. — Italy takes the lead of European 
nations, with an average annual crop of murders of 
2470, a ratio per 10,000 deaths of 29.4 ; Spain fol- 
lows, with a ratio of 23.8, and 1200 murders ; Aus- 
tria, ratio of 8.8, and 600 murders ; France, ratio of 
8.0, and 6G2 murders ; England, ratio of 7.1, and 
377 murders. The figures, however, represent 
actual murders, not homicides from all causes, as 
do those in the United States table. 

Illegitimacy. — Of each 1000 births, the number 
illegitimate, according to statistics published in 
London, 1892, were : Russia, 27 ; Ireland, 28 ; Hol- 
land, 33 ; England and Wales, 46 ; Switzerland, 47 ; 
Italy, 73 ; Norway, 74 ; Scotland, 79 ; Prussia, 80 ; 
France, 84 ; Hungary, 85 ; Belgium, 88 ; Denmark, 
93 ; Sweden, 101 ; Saxony, 125 ; Bavaria, 141 ; Aus- 
tria, 147. No accurate statistics for the United 
States exist. The lowest rate in Europe is that 
of Connaught, in Western Ireland, 7 per 1000. — 
Dr. Albert Leffingwell, Summit, N.J. 

3. When phenomena indicate a marked departure 
from the ratio of frequency as determined by prior 
observation, or by theoretical considerations, then 
it is ordinarily inferred that a new cause has be- 
come operative, not before existent, or, if present, 



244 INDUCTIVE LOGIC 

its effect neutralized. For instance, we would natu- 
rally expect a die to show the face three, on an 
average, about once in six throws. But if it re- 
peatedly turns up three in succession, and no other 
number appears, or appears but rarely, we are 
warranted in inferring that the die is loaded. 
The number of homicides in the United States in 
1894 far exceeded the annual number observed for 
the several years preceding. This discrepancy is 
easily accounted for by the fact that the natural 
number was swollen by the deaths caused by the 
strikers and rioters in the month of July of that 
year. So also a marked departure from the annual 
death-rate of such a city as New York is at once 
an urgent suggestion to the Board of Health to 
start investigations that will unearth the hidden 
cause that one is constrained to believe must be 
present. Such causes as defective drains, preva- 
lence of epidemics, etc., are again and again found 
to accompany an increase of the average death-rate. 
Under such circumstances, the method of investi- 
gation, when practicable, which should be pursued, 
is to endeavor to break up the total into smaller 
groups of a specific nature. Thus, if the death-rate 
for the year is appreciably increased, examine the 
death-rate per month. See if any month shows a 
marked departure from the average. If so, this 
will suggest a careful investigation of the circum- 
stances and characteristics of the month in question. 
Or it may be possible to make a geographical dis- 
tribution of the total over different sections of the 
city under investigation. Some special locality may 



PROBABILITY 245 

indicate an unusually large death-rate. Investiga- 
tion, therefore, at that point may reveal a lurking 
cause of disease, otherwise unnoticed. 

By similar considerations also, it is often possible 
to distinguish between a chance coincidence, and a 
determinate cause which has produced the event in 
question. For, if the possibility of some one defi- 
nite cause is considered out of the question, and 
the origin of the event is found among complex 
phenomena of such a number and variety that they 
may form an indefinite number of combinations, 
only one of which can possibly produce the event 
in question, then the probability that the event has 
actually been produced by such a chance combina- 
tion is extremely small. We are then thrown back 
upon the other hypothesis, that, instead of one out 
of many possible combinations, there is some one 
determinate cause operative in the case. Its nature 
may not be definitely indicated, but at least the 
possibility of its presence is suggested. 

This line of reasoning is illustrated in the fol- 
lowing account of the discovery of the existence of 
iron in the sun, in the researches of Bunsen and 
Kirchhoff : " On comparing the spectra of sunlight 
and of the light proceeding from the incandescent 
vapor of iron, it became apparent that at least sixty 
bright lines in the spectrum of iron coincided with 
dark lines in the sun's spectrum. Such coinci- 
dences could never be observed with certainty, 
because, even if the lines only closely approached, 
the instrumental imperfections of the spectroscope 
would make them apparently coincident, and if one 



246 INDUCTIVE LOGIC 

line came within half a millimetre of another, on 
the map of the spectra, they could not be pro- 
nounced distinct. Now the average distance of the 
solar lines on Kirchhoff's map is two millimetres, 
and if we throw down a line, as it were by pure 
chance, on such a map, the probability is about l 
that the new line will fall within one-half milli- 
metre on one side or the other of some one of the 
solar lines. To put it in another way, we may 
suppose that each solar line, either on account of 
its real breadth, or the defects of the instrument, 
possesses a breadth of one-half millimetre, and that 
each line in the iron spectrum has a like breadth. 
The probability, then, is just \ that the centre of 
each iron line will come by chance within one milli- 
metre of the centre of a solar line, so as to appear 
to coincide with it. The probability of casual coin- 
cidence of each iron line with a solar line is in like 
manner \. Coincidence in the case of each of the 
sixty iron lines is a very unlikely event if it arises 
casually, for it would have a probability of only 
(■!•) m or less than one in a trillion. The odds, in 
short, are more than a million million millions to 
unity against such a casual coincidence. But on 
the other hypothesis, that iron exists in the sun, it 
is highly probable that such coincidences would be 
observed ; it is immensely more probable that sixty 
coincidences would be observed if iron existed in 
the sun, than that they should arise from chance. 
Hence, by our principle, it is immensely probable 
that iron does exist in the sun." * 

1 Jevons, Principles of Science, pp. 244, 245. 



PROBABILITY 247 

This principle is also illustrated in instances of 
circumstantial evidence. In such cases, the observed 
combination of so many diverse circumstances, even 
as regards an indefinite number of minor details, 
precludes the hypothesis of casual coincidence, and 
suggests some one definite cause that will prove a 
unifying principle of explanation of all the attend- 
ant circumstances. As Mr. Justice Bullen says : 
" A presumption which necessarily arises from cir- 
cumstances is very often more convincing and 
more satisfactory than any other kind of evidence. 
It is not within the reach and compass of human 
abilities to invent a train of circumstances which 
shall be so connected together as to amount to a 
proof of guilt without affording opportunities to 
contradict a great part, if not all, of these circum- 
stances." 

The following account, taken from The New York 
Law Journal, illustrates the probative force of cir- 
cumstantial evidence : — 

In Nicholas v. Commonwealth (March 1895, 21 S. E. R. 
364) the Supreme Court of Appeals of Virginia sustained a 
conviction of murder, the criminal agency being established 
by circumstantial evidence. The following extract from the 
opinion presents the main facts which implicated the de- 
fendant : — 

" On the 8th day of December, 1802, Philip Norman 
Nicholas, the plaintiff in error, one James Mills, and his 
wife, Anna A. Mills, and their three small children, were 
living in the upper part of Henrico County, on a farm 
known as the ' Wickham Place,' about one mile from James 
River. Nicholas was the renter of this farm, and cultivated 
it on shares. He was himself, however, chiefly engaged as 



248 INDUCTIVE LOGIC 

a trapper, having a number of traps set along both sides of 
the river. He employed James Mills, with whom he lived, 
and one William Judson Wilkerson, as subtenants, to do 
the farm work, for a portion of his share of the crops. 
Wilkerson lived with an aged mother in a small house very 
near to Mills' house — near enough to see into the windows 
of one house from the other. Philip N. Nicholas, the pris- 
oner, was an unmarried man, and lived in a room of the 
house occupied by James Mills and his family. The evi- 
dence shows that on the night before the drowning, the 
prisoner, James Mills, and William J. Wilkerson were 
together at the house of Mrs. Wilkerson, the latter's 
mother, and there arranged and determined upon a trip 
across the river the next morning, to take a bee tree. This 
expedition was suggested, planned, and carried out by the 
prisoner. Wilkerson was very unwilling to go, and finally 
consented at the suggestion of his mother, who said that, as 
Mr. Nicholas seemed so anxious for him to go, he had better 
do so. Mills was unwilling to go unless Wilkerson went. 
Wilkerson said he would rather plough than go. The prisoner 
replied, ' If you will go, you shall not lose anything.' In the 
course of conversation which resulted in this expedition 
being agreed upon, both Mills and Wilkerson stated, in the 
presence of Nicholas, that they could not swim, and were 
very much afraid of water ; that they did not like water 
more than knee-deep. The fact that they could not swim 
was generally known to their friends. It is further shown 
that it was the habit of Nicholas to go every morning, early, 
to the river, to examine his traps. And it appears from the 
evidence that on the morning of the day the drowning 
occurred he went to the river about daylight, and returned 
about breakfast time, and, when questioned about it, said: 
'I did not go to my traps this morning. I was sick.' He 
afterwards told Mrs. Wilkerson he did not catch anything. 
Everything being in readiness to carry out the plan for the 
day, these three men started from home about nine o'clock 
in the morning, equipped with everything necessary for 



PROBABILITY 249 

taking the bee tree ; having with them two buckets holding 
two and one-half to three gallons each for the honey, two 
axes, one hatchet, and a piece of netting to protect the per- 
son from the bees. The boat used belonged to one Joseph 
Bruin, and on their way to the river an uncle of the owner 
was asked if they might use the boat, and was told they 
could get the key which unlocked the boat from its fastening 
to the bank from Bruin, the owner. The prisoner replied 
that he had a key of his own, and had often used it before 
without permission. It appears that they landed on the 
Chesterfield side of the river, at a point one mile and a half 
from where any one lived, and proceeded to the bee tree, 
which was one mile from the point of landing. Investiga- 
tion showed that there were no tracks about the point of 
landing but those of the three men going from and returning 
to the boat. It further appears from the statement of the 
prisoner that after reaching the tree they concluded not to 
cut it, because it was a large tree, near the main road, and 
might get them into trouble, and for the further reason that 
the hole was small, and it might not have any honey in it 
anyhow. The tree was afterwards cut by order of the Magis- 
trate and found to be full of honey. It further appears that 
the boat was a small one, about ten feet long and about two 
and one-half feet wide, and that both in going over and 
returning the prisoner sat in the extreme rear of the boat, 
with his face to the front, and that Wilkerson and Mills sat 
in front of him, with their faces to the front and their backs 
to the accused. This position of the parties the prisoner 
admitted very reluctantly, when questioned about it. When 
returning, and about fifty yards from the Henrico shore, 
the boat suddenly filled with water, and Mills and Wilker- 
son were drowned, and the prisoner swam to shore. The 
next day the Magistrate of the district was notified of the 
occurrence, and an investigation was set on foot. The boat 
was gotten out of the water, and it was found that immedi- 
ately under the seat where Nicholas sat there were three 
holes, freshly bored with an inch and a half auger. The 



250 INDUCTIVE LOGIC 

evidence of the owner of the boat shows that on Tuesday 
evening, the 6th of December, he used his boat, and it was 
sound. It was taken by Nicholas for this fatal trip Thurs- 
day morning, the 8th of December. Further investigation 
discovered fresh pine shavings corresponding to size of the 
holes and to the wood the boat was made of, which had 
been thrown into the water, but had drifted upon the shore 
near the point where the boat had stood fastened to the 
Henrico side. There were also found corn-cobs which had 
been cut to exactly fit the holes in the boat, which had also 
drifted to the same point. It was shown that the prisoner 
had in his possession an auger just the size of the holes. 
This the prisoner at first denied, but afterwards said that it 
must be about the place somewhere. Diligent search was 
made for the auger, but it was never found. 

" Taken together, the case is an interesting illustration of 
the conclusive probative force of circumstantial evidence, 
provided there is enough of it. The old saying that ' mur- 
der will out ' is almost unexceptionally true as to murders 
of elaborate stealth and complexity of detail. Once let a 
clue be obtained to the chain of causation and motive, and 
the mystery unravels almost of itself. It is quite natural 
that most of the elaborately planned murders of recent 
times should have been by poison. And the Harris, Buch- 
anan and Meyer cases in New York disclose how compara- 
tively easy detection and conviction are in crimes of such 
class. It is significant that two of the greatest enigmas in 
American criminal annals during the last quarter of a cen- 
tury have been the Nathan murder and the Borden murder. 
In both cases the killing was done not by methods calcu- 
lated to conceal the agency of a murderer, but in the most 
primitive and brutal manner. No traceable physical clue 
to any particular person was left, and we are inclined to 
believe that in both cases the connection of the murderer 
with the crime was merely casual or accidental." 1 

1 The New York Law Journal, Thursday, May 2, 1895. 



PROBABILITY 251 

In the various illustrations which have been given 
we find that the theory of probability provides a 
method of dealing with phenomena which cannot 
be subjected to the ordinary inductive methods. 
The phenomena are so complex that a specific cause 
cannot be determined, for the real cause in question 
is a correlation of many diverse forces, and if only 
a few instances are examined no causal connection 
will be disclosed ; it is necessary, therefore, to deal 
with large numbers, statistical averages, etc., in 
order to detect an emerging relation of a causal 
character, expressed by a constant ratio. This ratio 
once determined, it becomes a further test, as we 
have already seen, when the results widely depart 
from it, to suggest the presence of a new force out- 
side of the combinations to which the effect would 
be naturally referred according to the indications of 
the probability -ratio. This latter mode of inference 
is akin to the method of residues, for the inference 
in question is based upon the fact that the probabil- 
ity-ratio will account for only a certain frequency 
of occurrence of the event under investigation; a 
marked excess must be accounted for by positing a 
definitely operative cause. And if an antecedent 
of such a nature is known to be present, the sugges- 
tion at once rises in our thought that this in all 
probability is the cause producing this excess in the 
results. 



CHAPTER XVI 

Empirical Laws 

There is a class of laws which are intermediate 
between a universal, inductively grounded by scien- 
tific determination, and a law of tendency which is 
the expression of the probability of the happening 
of an event in spite of recognized exceptions. These 
are laws which have been observed to obtain under 
given conditions of time, place, and circumstance, 
and yet the causal relation not sufficiently deter- 
mined to warrant a necessary extension of the 
same to a sphere beyond that wherein it has been 
observed to be operative. Such laws are known as 
Empirical Laws. We have, therefore, three classes 
of laws of varying degrees of probability. The 
first is where there has been a scientifically deter- 
mined causal connection between antecedent and 
consequent ; and not only have no exceptions been 
noted, but the possibility of there being an excep- 
tion has been eliminated by strict experimental 
methods. The second is where the regularity of 
sequence has been broken by actual exceptions, and 
the result of the observations of instances gives an 
indication only of the relative frequency of occur- 
rence and failure which will probably characterize 
252 



EMPIRICAL LAWS 253 

other events of that nature. The third class and, 
as has been said, an intermediate class, comprises 
all expressions of uniform sequence or coexistence, 
where no exception whatsoever has been noted, and 
yet there is no ground for necessitating a universal 
expression of the observed uniformity. There is 
here always a possibility of an exception appearing, 
or of an exception having been overlooked. This 
produces an element of uncertainty which pervades 
all phenomena of this sort. 

There are several kinds of empirical laws, as 
follows : — 

1. Where the causal relation is in process of 
scientific determination ; a uniform connection 
between phenomena has been observed, and as 
yet has not been proved. All laws, finally deter- 
mined as expressions of causal connection, pass 
through this empirical stage. Some expressions 
of uniform relations never pass beyond this stage, 
because, as we have seen, the nature of the phenom- 
ena may be such as to preclude all experiment or 
even indirect verification. 

Empirical laws may become ultimate laws or 
derivative laws, as the case may be. Ultimate 
laws are those wherein the causal relation between 
a simple antecedent and its corresponding conse- 
quent has been scientifically determined in terms 
of their exact quantitative variation, and expressed 
in the simplest form possible. The derivative 
laws, however, as the name indicates, are more 
concrete expressions of the ultimate and simpler 
laws to which they are referred as special cases. 



254 INDUCTIVE LOGIC 

An empirical law may be proved directly an ulti- 
mate law, or be proved a derivative law directly 
traceable to an ultimate law, as its basis, or logical 
ground. We may observe that a glass of ice-water 
always shows drops of moisture on its outer sur- 
face. This uniformity as thus expressed has the 
force only of an empirical law. No attempt hav- 
ing been made, as yet, to explain the presence 
of the moisture, its empirical nature is evident. 
But as soon as the moisture on the glass is traced 
to the condensation of the moisture in the atmos- 
phere owing to the difference of temperature be- 
tween the atmosphere and the cold surface of the 
glass, we have the empirical law becoming a deriva- 
tive law; that is, the expression of a uniform 
sequence directly traceable to the more ultimate 
law of the saturation and condensation of vapors. 
The progress of scientific and logically accurate 
thought is always marked, therefore, by the resolu- 
tion of empirical generalities into derivative and 
ultimate laws. 

2. The character of an empirical law is attached 
to the relation existing between antecedent and 
consequent, when that relation is a complex one in 
which a simple causal relation is so involved with 
other elements entering into combination with it, 
that its real nature is thus hidden and cannot read- 
ily be disclosed. This class includes all causal rela- 
tions due to collocations of various kinds that are 
necessary to produce the required effect. As Mill 
has pointed out : " It is the nature of an empirical 
law that we do not know whether it results from 



EMPIRICAL LAWS 255 

the different effects of one cause or the effects of 
different causes. We cannot tell whether it depends 
wholly upon laws, or partly upon laws and partly 
upon a collocation. If it depends upon a colloca- 
tion, it will be true in all the cases in which that 
particular collocation exists. But since we are 
entirely ignorant, in case of its depending upon a 
collocation, what the collocation is, we are not safe 
in extending the law beyond the limits of time and 
place in which we have actual experience of its 
truth. Knowing of no rule or principle to which 
the collocations themselves conform, we cannot 
conclude that because a collocation is proved to 
exist within certain limits of place or time, it will 
exist beyond those limits." 1 

There are many illustrations of such observed 
generalities where the effect is due largely, if not 
altogether, to collocations. The effect of certain 
medicines upon the human system, the opening and 
shutting of some flowers at certain hours of the 
day, the local action of tides at various places on 
the earth's surface, the adaptation of certain plants 
to a peculiar kind of soil, the reappearance of some 
chronic diseases, as hay-fever, at the same season 
each year, even to the very day of the month, all 
such generalities have merely an empirical weight, 
and the effects mentioned are largely due to collo- 
cations that cannot be definitely determined. So 
also certain laws or customs may have proved 
beneficial in the countries in which they have been 
tried, and yet, in countries where condition and 

i Mill, Logic, Book III. Chapter XVI. § 4. 



256 INDUCTIVE LOGIC 

circumstance are radically different, they may fail 
wholly of beneficial results. There may be also 
certain industrial circumstances which in one coun- 
try might be conducive to prosperity, and in an- 
other country to adversity. Certain agricultural 
methods which in one section of the country tend 
to an increase of productive power, in another 
might prove a complete failure. A governmental 
policy may in one country lead to unparalleled suc- 
cess ; in another, however, a like policy might lead 
to disastrous results. 

The famous formula of Malthus, that population 
tends to increase in a geometrical progression, whilst 
the means of subsistence can only increase in an 
arithmetical progression, can have only an empirical 
force. Its extension into an indefinite future is 
unwarrantable. As is known, production has in- 
creased enormously and at a ratio vastly greater 
than any contemplated by Malthus as at all in the 
range of possibility. Many causes, on the other 
hand, may combine to check the rapid increase of 
population. The collocations here are so complex 
as to defy any definite prediction. This is true of 
all tendencies which are due to present social con- 
ditions ; the conditions themselves may so vary in 
time to come as to change totally the accepted 
generalizations of to-day. Their empirical character 
is, therefore, most evident. 

3. A third class of empirical laws comprises all 
those generalizations which represent an aggregate 
of properties in the same individual. In all such 
cases no causal relation has been specifically de- 



EMPIRICAL LAWS 257 

termined between the properties themselves, or 
between the properties and the whole in which they 
coinhere. Outside of our experience, the proper- 
ties observed might be materially changed, and yet 
not affect the integrity of the concept in general. 
A proposition such as all swans are white can have 
only empirical force; for beyond our experience, 
the discovery of black swans would forbid the prop- 
osition being regarded in the light of a universal. 
Many properties of substances are thus referred to 
the nature of the substance itself as their ground, 
and yet because the exact causal relation is not de- 
termined the connection can be considered only as 
an empirical one. In other words, reference to some 
ground as explanation of a phenomenon, without 
explaining why or how such reference is made, has 
always the force of an empirical law only. The fol- 
owing are empirical generalizations of this nature. 
Copper is ductile ; steel is elastic ; glass is brittle and 
transparent ; the compound silicates of alkalies and 
alkaline metals are transparent ; and other instances 
of like nature that can be multiplied indefinitely. 

In the sphere of biology, Mr. Spencer has drawn 
attention to the fact that " during the era in which 
uniformity of many quite simple inorganic rela- 
tions was still unrecognized, certain organic rela- 
tions, intrinsically very .complex and special, were 
generalized. The constant coexistence of feathers 
and a beak, of four legs with an internal bony 
framework, are facts which were, and are, familiar 
to every savage. Did a savage find a bird with 
teeth, or a mammal clothed with feathers, he would 



258 INDUCTIVE LOGIC 

be as much, surprised as an instructed naturalist. 
Now these uniformities of organic structure, thus 
early perceived, are of exactly the same kind as 
those more numerous ones later established by 
biology. The constant coexistence of mammary 
glands with two occipital condyles to the skull, 
of vertebrae with teeth lodged in sockets, of frontal 
horns with the habit of rumination, are generaliza- 
tions as purely empirical as those known to the 
original hunter. The botanist cannot in the least 
understand the complex relation between papilio- 
naceous flowers and seeds borne in flattened pods ; 
he knows these and like connections simply in the 
same way that the barbarian knows the connections 
between particular leaves and particular kinds of 
wood." * Such knowledge as Mr. Spencer here de- 
scribes is a knowledge of the coexistence of two 
phenomena in their totality which resist all at- 
tempts to analyze into their component parts. 
Moreover, laws which are but general descriptions 
of correlated events have the same force as the 
descriptions of coinhering attributes of substances. 
They, too, rank as empirical generalizations. The 
successive stages in the growth of a plant from 
seed to flower and fruit, the embryonic as well as 
the post-natal developments in animal life, the 
habits and instincts of animals, — all these are de- 
scriptive generalizations without any attempt at 
causal determination. 

4. All generalizations expressed in terms of prob- 
ability only, because of known exceptions, rank as 

1 Spencer, Classification of the Sciences, p. 53. 



EMPIRICAL LAWS 259 

empirical laws. Here, even in the time, place, and 
circumstance of observation, the law has not been 
found, always valid.. The significance of an empiri- 
cal law, if we allow this latter class to be included 
under them, is evidently that of the contradictory 
of a law which is the result of a causal determi- 
nation. Every generalization not causally deter- 
mined is then to be regarded as an empirical law. 
There is, however, a narrower usage of the term 
which does not include this latter class ; namely, 
a restriction of the term empirical law to signify 
the expression of a relation which has been found 
constant throughout the sphere of observation, and 
yet where there exists no known causal ground by 
reason of which we would be warranted in infer- 
ring the continuation of this relation in a sphere 
beyond that already observed. We might add that 
with this there is also the expectation, greater or 
less, according to the circumstances attending the 
phenomena, that the generalized experience •will 
be further confirmed by subsequent observation in 
a wider sphere. This restricted meaning of an em- 
pirical law is the one generally understood, unless 
it is implied to the contrary. 

An empirical uniformity generally results from 
the method of agreement. Observed instances, 
even so selected as to ■ vary the antecedents as 
much as possible, cannot alone establish a law 
of uniformity that shall have universal validity. 
The method of agreement, we have seen, needed to 
be supplemented by the method of difference if 
possible, or by an hypothesis capable of subse- 



260 INDUCTIVE LOGIC 

quent verification. An empirical law is, therefore, 
due either to some deficiency in method, or to the 
natural limitations of our knowledge. 

The element of uncertainty attached to all infer- 
ences depending upon the extension of an empirical 
law into unknown territory, it has been insisted 
upon in several quarters, may apply equally as well 
to all inferences depending upon the results of the 
inductive methods even when most scientifically 
determined. It is contended that even a causal 
relation, however firmly grounded, and however 
simple may be its nature, nevertheless presents an 
empirical character. It may give assurances of a 
high degree of probability, but can never produce 
absolute certitude in our minds. Mr. Venn, for in- 
stance, has styled his work on induction Empirical 
Logic, that by the title he might indicate his point 
of view in this regard. He says in the preface to 
his work : " By the introduction of the term empir- 
ical into the title, I wish to emphasize my belief 
that no ultimate objective certainty, such as Mill, 
for instance, seemed to attribute to the results of 
induction, is attainable by any exercise of the hu- 
man reason." Regarded in this light, all laws are 
empirical. 

The distinction, however, between empirical laws 
in the sense generally understood, and laws ex- 
pressing causal relations scientifically determined, 
is a real distinction, and a significant one as well. 
And this must not be overlooked; and it cannot 
be obliterated by any shifting of the point of 
view. For, to doubt the validity of an empirical 



EMPIRICAL LAWS 261 

law when extended to a sphere beyond that which 
has been observed, casts a reflection merely up- 
on one's ability adequately to determine the con- 
nections existing between the various elements 
involved in the particular phenomena under in- 
vestigation. This is, however, no confession of 
inability to discover the causal connections of 
phenomena in general, in such a manner as to 
determine laws of universal validity. To say that 
all laws have only empirical significance is to re- 
flect upon the basal postulates of knowledge. Our 
world is the world as we know it, the world of our 
consciousness. To discredit the uniformities and 
regularities therein existing, and which find ex- 
pression in universal laws, is to discredit that 
which we feel obliged to think in order that our 
world of knowledge, regarded as a system, may 
remain consistent with itself, that is, part to part, 
and part to whole. We must, therefore, regard 
an empirical law not as the final form of knowl- 
edge, or the goal of inductive research, but rather 
as marking a transition stage towards complete 
causal determination. And even when, owing to 
the nature of certain phenomena, we are not able 
to pass beyond this transition stage of empirical 
determination, nevertheless, such instances by con- 
trast bear unimpeachable testimony to the fact 
that there are other phenomena of such a nature 
that it is possible to subject them to an analysis 
which will disclose causal connections of such a 
character as to form a basis for the formulation of 
universal laws. 



CHAPTER XVII 

Fallacies 

A consideration of the various kinds of induc- 
tive fallacies, and their characteristic features, may 
be regarded as the obverse representation of the 
general theory of induction. From the one point 
of view we consider the positive conditions of true 
inductive inference ; from the obverse point of view 
we regard the various breaches of these inductive 
conditions. The discussion of fallacies, therefore, 
indicates no progress in the elucidation of the sub- 
ject under consideration ; it rather serves to empha- 
size distinctions and requirements already indicated 
by presenting them in a new light and from a dif- 
ferent angle. The subject of fallacies is generally 
treated by exhibiting through various illustrations 
the cases in which the positive conditions of induc- 
tive inference have failed of satisfactory fulfilment. 
Such illustrations of the infringement of the require- 
ments of valid induction, I have endeavored to 
incorporate in the body of the text in connection 
with the exposition of the various conditions and 
requirements themselves. In this chapter I shall 
attempt to indicate those fallacies especially which 
are due to the psychological disturbance of our 
262 



FALLACIES 263 

normal logical processes. An enumeration of these 
tendencies, partly psychological and partly logical, 
may serve to impress upon us the danger of falling 
into easy errors, to which the human mind generally 
is liable. These errors emerge in the various mental 
processes. They are as follows : — 

I. Errors of Perception. 
II. Errors of Judgment. 

III. Errors of the Imagination. 

IV. Errors of the Conceptual Processes. 

I. Errors of Perception. — Observation is the in- 
strument of research pre-eminently, in all inductive 
inquiry. Experiment is but a method for increased 
facility and accuracy of observation. We may say, 
therefore, that all the data of inductive inference 
are furnished by this one process, observation. Any 
derangement of our powers of observation will affect 
the nature of the data, and therefore the nature of 
the results of induction. It becomes, therefore, all 
important that we should be appraised at least of 
the various circumstances whose tendency is to 
operate in the midst of the perceptive processes as 
disturbing forces. We have the following possibili- 
ties of error in the sphere of perception : — 

1. Errors due to a failure to take in the whole 
field of vision. There may be portions omitted 
which possess a determining significance as regards 
the object of investigation. Thus exceptions may 
be overlooked that might have an important bearing 
upon some received hypothesis; or a fact might be 
passed by which, if known, would prove highly sug- 



264 INDUCTIVE LOGIC 

gestive. Various devices have been employed to 
enlarge the sphere of observation beyond the natu- 
ral limits of the senses. As, for instance, sounds 
which are inaudible to us may be detected by means 
of a sensitive flame ; the telescope, the microscope, 
serve to render the distant near, and the small 
large. It had been noted that there was a sudden 
elongation of an iron wire at a particular tempera- 
ture whilst under longitudinal strain during the act 
of cooling from a red heat ; an additional circum- 
stance was noted by Professor Barrett when per- 
forming the experiment in a darkened room, namely, 
that at the moment of elongation the wire suddenly 
evolved heat, and exhibited a visible and conspicu- 
ous momentary glow of redness. 1 This circum- 
stance it would be impossible to note unless in a 
darkened room. Thus, a prominent characteristic 
of scientific observation is the endeavor to extend 
continually the sphere of observation. Here also 
much depends upon the mental habit. There are 
some who naturally see wider and farther than 
others. And it is absolutely necessary that the 
true observer should cultivate with all assiduity 
such a habit when it is not a natural possession. 
There is a slovenliness in observation which gives 
to the inferences based upon its results a color of 
indefmiteness and inaccuracy, and which proves a 
fertile source of error. 

It also often happens, that, owing to the mind 
being prepossessed by a certain idea or theory, re- 
search will be thereby restricted to a limited region, 

1 Gore, The Art of Scientific Discovery , p. 321. 



FALLACIES 265 

and neighboring regions be wholly overlooked. 
An open-eyed vision, in spite of all preconceptions 
or prejudices, is the prime requisite for securing 
from all quarters the greatest possible array of 
facts that may in any way tend to the formation 
of a clearer and more adequate judgment. 

2. A second error of observation arises from an 
opposite mental habit, a failure properly to concen- 
trate the attention upon the relevant facts and so 
to discriminate as to exclude from consciousness, for 
the time being at least, all irrelevant details. The 
lack of such a discriminating faculty leads either 
to error, or to the dearth of all significant results. 
It is necessary to avoid either extreme, so that there 
may be a sweeping survey of all the possible facts 
relevant to the subject under investigation, com- 
bined at the same time Avith a concentration of 
attention that is the prerequisite of a deep insight 
into the inner connections and interrelations of 
these facts. There must be a depth as well as a 
wideness of vision. 

There are also errors arising from a failure to 
note significant differences in phenomena that 
present striking surface resemblances. Here the 
closest scrutiny is necessary. The older chemists 
could not distinguish potash from soda ; baryta and 
strontia were formerly confounded together, so also 
potash and cassia. Throughout the whole realm of 
scientific research, it should be ever kept promi- 
nently in mind that surface differences may hide 
essential resemblances, and that surface resem- 
blances may hide essential differences. 



266 INDUCTIVE LOGIC 

3. Errors may arise from apperceptive projection. 
Here the objective elements of perception combine 
with the subjective, so that the complete perception 
may contain elements which do not correspond with 
reality. The mind thus projects upon the field of 
vision its own coloring. We see often that which 
we wish to see, and fail to see that which we do not 
wish to see. When palladium was originally made 
known to the public, Chenevix proceeded to examine 
it, prepossessed with the idea that it was an alloy of 
some two known metals. This idea was so projected 
upon his experiments, that he at last came to the 
conclusion that it was a compound of platinum and 
mercury. Chenevix was led into an error of obser- 
vation, as was afterwards proved by Dr. Wollaston, 
who himself had obtained palladium from the solu- 
tion of crude platina in aqua regia. 1 This error of 
observation was due to the fact that he approached 
the experiments with a fixed idea in his mind as to 
what they should prove ; and being determined to 
see evidences of this in the phenomena, he uncon- 
sciously read into them that which was not really 
there. 

II. Errors of Judgment. — These errors occur in 
the interpretation of the data of perception. For 
that which is observed must be referred to its 
appropriate place in the body of knowledge re- 
garded as a system, in which, part must fit to part, 
and part to whole. Inaccurate reference results in 
manifest imperfections and incongruities in that 
part of the system of knowledge to which the ref- 

i Gore, The Art of Scientific Discovery. 



FALLACIES 267 

erence has been made. And the inferences based 
thereupon are naturally affected by this funda- 
mental error of judgment. These errors are as 
follows : — 

1. Errors due to false associations. Here, where 
artificial or superficial associations are interpreted 
as though they were real causal connections, the 
mistake may prove most serious. The most fertile 
source of such fallacies is the wrong interpretation 
of space and time associations, regarding mere con- 
tiguity in space and time as evidence of causal 
connection. Under this' head may be classed the 
fallacies, rum causa pro causa, and post hoc ergo 
propter hoc. Prosperity, for instance, following the 
enactment of certain industrial or tariff measures, 
is often attributed as the effect of the same, merely 
because they appear in striking sequence. How- 
ever, it may be that the prosperity has followed in 
spite of the laws and not on account of them. 

2. Errors of judgment due to. emotional pertur- 
bations. When the intellect is deflected from its 
true pointing by passion, or prejudice, or super- 
stition, or any strong emotion, the consequent 
judgment is the resultant of two forces, rather 
than the expression of one. As Bacon says: "The 
human understanding resembles not a dry light, but 
admits a tincture of the will, and passions which 
generate their own systems accordingly ; for man 
always believes more readily that which he prefers ; 
his feelings imbue and corrupt his understanding in 
innumerable and sometimes imperceptible ways." 1 

1 Bacon, Novum Organon, Book I. Aphorism XLIX. 



268 INDUCTIVE LOGIC 

The necessity of judging in a " dry light," as far 
as possible, is especially emphasized in the ethical 
positions of Adam Smith, and later of Mr. Sidgwick. 
Adam Smith contends that one's duty must be 
estimated from the standpoint of an impartial 
spectator and critic. That is, man must, as it 
were, step out of himself, leaving feeling behind, 
and judge of himself and of his duty from a 
purely objective point of view. So also Mr. Sidg- 
wick says that one of the chief difficulties in the 
utilitarian position, namely, the discrepancy be- 
tween the egoistic and altruistic claims upon 
our activities, cannot be harmonized satisfactorily, 
when stated as a problem of mere feeling. Here 
again man must eliminate feeling and judge of 
himself merely as one among many, where each 
counts for one and no one for more than one. In 
the light of pure reason he may be able to see 
that the good of all is his highest good. But 
when that dry light is colored by feeling, such 
judgment is impossible. 

Faraday, in his Observations on Mental Education, 
has borne testimony directly to the necessity of 
eliminating feeling from our judgments. He says : 
"The tendency to deceive ourselves regarding all 
we wish for should be kept in mind, and the neces- 
sity also of resistance to these desires. The force 
of the temptation which urges us to seek for such 
evidence and appearances as are in favor of our 
desires, and to disregard those which oppose them, 
is wonderfully great. In this respect we are all 
more or less active promoters of error. I will 



FALLACIES 260 

simply express my strong belief that that point of 
self-education which consists in teaching the mind 
to resist its desires and inclinations until they are 
proved to be right, is the most important of all, 
not only in things of natural philosophy, but in 
every department of daily life." 1 

3. Errors of judgment due to the common frail- 
ties of human nature. Such errors Bacon has styled 
"Idols." His enumeration is not only complete, 
but is classic in its way, and therefore I quote it at 
this place : " Four species of idols beset the human 
mind, to which, for distinction's sake, we have as- 
signed names, calling the first Idols of the Tribe, 
the second Idols of the Den, the third Idols of the 
Market, the fourth Idols of the Theatre. 

"The formation of notions and axioms on the 
foundation of true induction is the only fitting 
remedy by which we can ward off and expel these 
idols. It is, however, of great service to point them 
out ; for the doctrine of idols bears the same rela- 
tion to the interpretation of nature as that of the 
confutation of sophisms does to common logic. The 
idols of the tribe are inherent in human nature, and 
the very tribe or race of man ; for man's sense is 
falsely asserted to be the standard of things ; on 
the contrary, all the perceptions, both of the senses 
and the mind, bear reference to man and not to the 
universe, and the human mind is like those uneven 
mirrors which impart their own properties to dif- 
ferent objects from which rays are emitted, and 
distort and disfigure them. 

1 Gladstone, Michael Faraday, p. 128. 



270 INDUCTIVE LOGIC 

" The idols of the den are those of each individual ; 
for everybody (in addition to the errors common to 
the race of man) has his own individual den or 
cavern which intercepts and corrupts the light of 
nature, either from his own peculiar and singular 
disposition, or from his education and intercourse 
with others, or from his reading, and the authority 
acquired by those whom he reverences and admires, 
or from the different impressions produced on the 
mind as it happens to be preoccupied and predis- 
posed, or equable and tranquil, and the like; so 
that the spirit of man (according to its several dis- 
positions) is variable, confused, and as it were actu- 
ated by chance ; and Heraclitus said well that men 
search for knowledge in lesser worlds, and not in 
the greater or common world. 

"There are also idols formed by the reciprocal 
intercourse and society of man with man, which we 
call idols of the market, from the commerce and 
association of men with each other; for men con- 
verse by means of language, but words are formed 
at the will of the generality, and there arises from 
a bad and unapt formation of words a wonderful 
obstruction to the mind. Nor can the definitions 
and explanations with which learned men are wont 
to guard and protect themselves in some instances, 
afford a complete remedy, — words still manifestly 
force the understanding, throw everything into con- 
fusion, and lead mankind into vain and innumer- 
able controversies and fallacies. 

"Lastly, there are idols which have crept into 
men's minds from the various dogmas of peculiar 



FALLACIES 271 

systems of philosophy, and also from the perverted 
rules of demonstration, and these we denominate 
idols of the theatre ; for we regard all the systems 
of philosophy hitherto received or imagined, as so 
many plays brought out and performed, creating 
fictions and theatrical worlds. Nor do we allude 
merely to general systems, but also to many ele- 
ments and axioms of sciences which have become 
inveterate by tradition, implicit credence, and neg- 
lect." 1 

All such tendencies, as thus presented by Bacon, 
clog and hamper the normal functioning of the 
judgment. The mind must be alert and on guard 
to eliminate such fatal seeds of error. 

III. Errors due to the Imagination. — Here the 
imagination supplies inner connections and rela- 
tions, lying beyond the sphere of observation, in 
order to explain the nature of the observed phe- 
nomena themselves. The danger here is that the 
elements supplied in order to make the self -con- 
sistent whole do not correspond to reality. The 
system, regarded as a mental construction, may be 
complete in all of its co-ordinated parts, and never- 
theless possess no objective reality. Under this 
head fall all loosely constructed hypotheses. In the 
framing of an hypothesis in general, the imagina- 
tion functions very largely. It is the inner vision 
that represents to the mind the things not seen. 
Moreover, the imagination is peculiarly liable to 
error, and to swing clear of the trammels of fact, 
and in the region of pure fancy construct systems 

1 Bacon, Novum Organon, Book I. Aphorisms XXXIX. etc. 



272 INDUCTIVE LOGIC 

that rest upon no solid basis of reality. These 
dangers in detail have been pointed out in the 
chapter on "Hypothesis." 

The most fertile source of error, however, arises 
from that natural elation of mind upon the discov- 
ery even of slight confirming evidence of the truth 
of the assumed hypothesis. This enthusiasm is apt 
to magnify unduly an inadequate verification, and 
to rest satisfied in an hypothesis that is grounded 
upon an insufficient basis. Thus since the year 
1770 more than forty discoveries of new elementary 
substances have been announced to the world by 
enthusiastic experimenters, and, in all cases, their 
discoveries have been proved to be absolutely worth- 
less. For instance, it was confidently announced 
that Torbern Bergmann, in 1777, had extracted from 
diamonds what he considered to be a new earth, 
and called it " terra nobilis." Wedgwood, in 1790, 
discovered " australia " in sand obtained from the 
continent of that name ; but Hatchett proved it 
to be merely a mixture of silica, alumina, oxide of 
iron, and plumbago. In 1805 Richter discovered 
" niccolanium " ; it was afterwards proved to be a 
mixture of iron, cobalt, nickel, and arsenic. These 
instances are but a few of the many which charac- 
terize the history of chemical research, and stand 
as conspicuous witnesses of the danger of divorcing 
fancy from fact. 

The imagination, however, properly constrained is 
most potent in suggesting possible causal relations, 
in constructing hypotheses, in devising methods of 
experiment in order to verify them, and in forming 



FALLACIES 273 

universal concepts in which all the particulars of 
observation must coinhere. Davy and Faraday 
were both conspicuous in this mental characteristic. 
And to this source their eminent discoveries may be 
traced. Dr. Whewell says, for instance, of Fara- 
day : " In discovering the nature of voltaic action, 
the essential intellectual requisite was to have a dis- 
tinct conception of that which Faraday expressed 
by the remarkable phrase, 'An axis of power hav- 
ing equal and opposite forces.' And the distinctness 
of this idea in Faraday's mind shines forth in every 
part of his writings. He appears to possess the 
idea of this kind of force with the same eminent 
distinctness with which Archimedes in the ancient 
and Stevinus in the modern history of science pos- 
sessed the idea of pressure, and were thus able to 
found the idea of mechanics. And when Faraday 
cannot obtain these distinct modes of conception, he 
is dissatisfied and conscious of defect." 1 

It is indeed a touch of genius that enables one to 
grasp and formulate a central idea that will unify 
and also universalize a large body of seemingly dis- 
connected and incongruous facts. But such an idea 
must be the expression of the relations actually ob- 
taining, and no subjective fancy projected upon the 
phenomena themselves, however clever or ingen- 
ious such an imaginative creation may be. If one 
were asked what is the most efficient instrument 
of scientific research, the answer must be, "The 
Imagination ! " And if one were asked what is the 

1 Whewell, History of Inductive Sciences, Vol. III. 3d ed., 
p. 147. 

T 



274 INDUCTIVE LOGIC 

most fertile source of error, the answer likewise 
must be, " The Imagination ! " It must also be 
remembered that it is not sufficient merely that an 
hypothesis should be in harmony with the facts in 
the case ; it must be proved also that the facts are 
connected with the hypothesis through necessary 
links. 

And it is well also to bear this in mind when 
arguing against a rival hypothesis that may have 
been advanced by an opponent who has claimed for 
it only the possibility of its validity, and who has 
not affirmed its necessity. It is manifestly unfair, 
as well as fallacious, to deny the possibility of the 
hypothesis merely by indicating certain uncertain- 
ties connected with establishing it. To contradict 
possibility, one must prove the hypothesis im- 
possible. Regarding such a conflict between rival 
hypotheses Ueberweg suggestively comments as 
follows : " In cases of this kind, it is one of the 
hardest of scientific and ethical problems to give 
fair play to one's opponent. Our own prejudices 
are sure to influence us. Yet the effect of the influ- 
ence of another's standpoint, when it is reached, is 
of immense value in scientific knowledge. Polemic 
easily leads to exasperation; it is easy both to 
abuse it, and to let it alone because of dislike to 
the conflicts which it produces; but it is difficult 
to recognize it, and use it in the right sense as the 
necessary form which the labor of investigation 
always takes. Man never attains to a scientific 
knowledge of the truth without a rightly conducted 
battle of scientifically justifiable hypotheses, the one 



FALLACIES 275 

against the other : the scientific guidance of this 
battle is the true dialectic method." 1 

IV. Errors of the Conceptual Processes. — This 
class of errors arises in the formation of general 
concepts and their expression in universal laws. 
The natural tendency of the mind to generalize 
often leads to ill-considered results. The universal 
unites many differences into an identity, and the 
mind will readily minimize the differences in order 
to form a desired universal; thus disparate attri- 
butes may be incorrectly co-ordinated in one and 
the same system. Herschel has remarked that 
hasty generalization is the bane of science. And 
Bacon has said our intellects want not wings, but 
rather weights of lead to moderate their course. 

The method of agreement, when relied upon to 
the exclusion of further experimental determina- 
tion, is a fertile source of error in this respect. The 
possibility of a plurality of causes should be ever 
kept prominently in mind. One readily assigns an 
effect to a causal element which is only partially 
its cause; the consequent generalization is, there- 
fore, incorrect. For instance, it often happens that 
activities of young animals are described as instinc- 
tive and congenital ; and universal propositions are 
founded thereupon. And yet it may be that the 
activities referred solely to instinct are due par- 
tially to imitation. In order to avoid this error 
and eliminate the factor of imitation, investigators 
in this line are accustomed to study the activities 
of animals hatched in incubators and purposely 
1 Ueberweg, A System of Logic, etc., p. 509. 



276 INDUCTIVE LOGIC 

kept from all of their kind. This illustration will 
serve to show the precautions that must be taken 
in order to eliminate all . possible error from the 
data which the process of generalization constructs 
into universal forms. So also inaccuracies in any. 
of the other inductive methods lead to gross errors 
in the consequent generalizations based upon them. 
Under this head, also, are the fallacies resulting 
from the extension of empirical laws to spheres 
beyond the experience which they embody and 
express. This source of error is especially illus- 
trated in laws expressing some quantitative relation 
between antecedent and consequent ; it is a natural 
supposition in such cases, and yet a very mislead- 
ing one oftentimes, that a simple proportional rela- 
tion will exist between phenomena of the same, 
but with greater or lesser magnitude as the case 
may be. Bacon gives the following illustrations of 
this fallacy : " Suppose a leaden ball of a pound 
weight, let fall from a steeple, reaches the earth in 
ten seconds, will a ball of two pounds, where the 
power of natural motion, as they call it, should be 
double, reach it in five? No, they will fall almost 
in equal times, and not be accelerated according to 
quantity. Suppose a drachm of sulphur would 
liquefy half a pound of steel, will, therefore, an 
ounce of sulphur liquefy four pounds of steel ? It 
does not follow ; for the stubbornness of the matter 
in the patient is more increased by quantity than 
the activity of the agent. Besides, too much as 
well as too little may frustrate the effect, — thus, 
in smelting and refining of metals it is a common. 



FALLACIES 277 

error to increase the heat of the furnace or the 
quantity of the flux ; but if these exceed a due 
proportion, they prejudice the operation because 
by their force and corrosiveness they turn much of 
the pure metal into fumes, and carry it off, whence 
there ensues not only a loss in the metal, but the 
remaining mass becomes more sluggish and intract- 
able. Men should, therefore, remember how iEsop's 
housewife was deceived, who expected that by 
doubling her feed her hen should lay two eggs a 
day ; but the hen grew fat and laid none. It is 
absolutely unsafe to rely upon any natural experi- 
ment before proof be made of it, both in a less and 
a larger quantity." l 

Another fallacy of the same order often occurs in 
the inference concerning the interpolated elements 
of a series whose successive values have not all been 
observed. The inference extends the nature of the 
known to the unknown parts, and presumes that 
the intermediate links between actually observed 
parts of the series are in accordance with the 
general nature of the latter. Such inferences very 
often give correct results, as, in the plotting of a 
curve, some salient points may be determined ac- 
cording to observed quantitative variations, and the 
remaining portions supplied, as upon the above 
supposition. This extension to cover intermediate 
and unobserved instances may, however, be some- 
times very fallacious. For a force may be assumed 
to be such that its effects increase steadily, and it 

1 Bacon, Advancement of Learning, Book V. Chapter II. 
p. 190. 



278 INDUCTIVE LOGIC 

may be that they operate periodically ; interpola- 
tion upon one assumed basis when the other is the 
true one, would of course introduce grave errors. 
To eliminate such errors, devices have in many 
cases been resorted to by which a self-registering 
apparatus will record all successive values of the 
phenomena under investigation. 

Under the fallacies of hasty generalization, nat- 
urally fall all provincialisms which arise from a 
narrow nature and habit of mind. The local tradi- 
tions and superstitions, the prevailing winds, the 
social customs and manners, are taken as types of a 
universal experience. The inferential widening of 
the circle of a limited experience is always provo- 
cative of false inference and misleading results. 

We have also false analogies which consist in the 
extension of our experience of certain phenomena 
that we have observed to be alike in some respects 
to include other attributes not observed, concern- 
ing which we assume a corresponding similarity; 
the abuse of final causes may be regarded as a 
special case of false analogy. Moreover, a tendency 
to consider causation in the light exclusively of final 
causes has often retarded the advance of science, in 
withdrawing the attention and energies of the in- 
vestigator from a search after physical causes, as, for 
instance, among the ancients it was declared that 
the leaves of the trees are to defend the fruit from 
the sun and wind. Resting satisfied in such an 
explanation, the precise function of the leaves in 
the economy of the plant's growth was not further 
investigated, and thus progress was impossible. 



FALLACIES 279 

Again, incorrect classification is a source of error. 
In grouping together disparate phenomena, we have 
a basis for forming a generic concept that will in- 
clude incompatible species, or, in other words, a 
universal that will have evident exceptions. More- 
over, if the classification is partial, the resulting 
laws based upon it will have only empirical force. 

I have endeavored in this chapter to indicate 
errors that are mainly psychological in their origin, 
for two reasons. In the first place, such errors 
operate as disturbing forces in the midst of purely 
logical processes. The data of inference are psy- 
chological as regards their source, and errors thus 
originating affect the inference based upon them, 
appearing in the final result as logical fallacies. 
An error of observation becomes an error in the 
judgment that is based upon the original percep- 
tion, and perdures in the hypothesis, classification, 
etc., founded on that judgment, and finally emerges 
in the conclusions based upon these processes. In 
the second place, the fallacies that are purely 
formal, and in the strict sense logical, are not as 
apt to deceive and mislead the mind. In the 
material data especially lurk the germs of fallacy. 
On the theory that it is wiser and also more logical 
to stamp out an error in its incipiency, I have 
placed special emphasis upon the various psycho- 
logical processes as initial sources of error. More- 
over, it is more rational to deal with errors of pro- 
cess rather than flaws of product. A machine that 
turns out imperfect articles could have its imperfec- 
tions rectified by repairing each article thus pro- 



280 INDUCTIVE LOGIC 

duced; or the machine itself could be readjusted 
so as to produce the articles without flaw. It is 
needless to say which method is the more logical, 
and most satisfactory, as well. 

The desideratum is accurate and comprehensive 
observation ; a discriminating judgment formed in 
the " dry light " of reason ; an imagination that has 
deep insight into the heart of surface appearances ; 
and powers of generalization which transcend ob- 
served phenomena by adequately interpreting them. 



CHAPTER XVIII 

The Inductive Methods as Applied to the 
Various Sciences 

The nature of each separate science will deter- 
mine certain peculiarities of method for that sci- 
ence ; and its peculiar method will be largely a 
matter of growth, as experience accredits or dis- 
credits the various results which its operation may 
attain. It will thus be corrected or supplemented 
according as it stands the test of achieved results. 
There are, however, some general features, and es- 
pecially some natural limitations of the inductive 
methods, that may be properly indicated. 

I. In the first place, the nature of the method 
used, and its efficiency, as measured by its results, 
will be found to vary as the nature of the phe- 
nomena themselves. Some phenomena admit of 
analysis and further determination by experiment. 
Instead of attempting to determine the relation of 
a complex antecedent to a complex consequent, the 
antecedent is first separated into its component 
parts, and one element is tested alone in order to 
determine its precise effect. The relation can then 
be expressed between the simple antecedent and 
simple consequent, as a causal connection; and it 
281 



282 INDUCTIVE LOGIC 

admits, moreover, of a quantitative determination as 
well. Such a method of procedure by analytical ex- 
periment enables us to rise to laws having universal 
validity. This method is characteristic, especially, 
of the physical sciences, because the phenomena 
readily admit of resolution into component parts, 
and the isolation of one simple force so as to de- 
termine its total effect. The physical forces are 
most readily adaptable to experiment. They there- 
fore afford the widest field for the application 
of the experimental method of inductive inquiry. 
Moreover, we may readily predict the results of a 
combination of simple forces, when we know the 
laws governing their component elements. The 
inducto-decluctive method, therefore, becomes es- 
pecially efficient in extending the domain of the 
physical sciences. Here, also, mathematical analy- 
sis and calculation is most valuable as an aid to 
experimental investigation, and in determining 
quantitative relations as necessitated by the math- 
ematical laws to which the data gathered induc- 
tively must conform. 

There are, however, sciences which present phe- 
nomena of such a high degree of complexity that 
an analysis of a complex whole into its separate 
parts or elements of force is impossible. More- 
over, the phenomena cannot be analyzed in this 
respect either, that a certain part of the complex 
whole can be indicated as the whole antecedent, 
and the remaining portion as the entire conse- 
quent. The difficulty, therefore, is twofold; it 
is impossible to separate the complex whole into 



INDUCTIVE METHODS AND THE SCONCES 283 

two other complex wholes, antecedent and conse- 
quent, and still further impossible to separate such 
antecedent and consequent, even if they could be 
determined, into their simplest component parts. 
The phenomena presented are here not in the 
form of a sequence so often as in that of coexist- 
ence, as in the sciences of botany, zoology, and the 
like. Here the methods of analogy and classifica- 
tion must be resorted to, and we obtain descriptive 
laws as the result. 

The forces manifested in the processes of vital 
growth are especially difficult to determine by ex- 
periment ; for they not only operate to produce 
certain effects, but perdure in the effects to pro- 
duce certain other effects in a process of con- 
tinuous construction. Separation by mechanical 
analysis means instant cessation of the process 
itself. Dissection means death. Here, then, is a 
natural limitation. Moreover, the laws of devel- 
opment are further modified by external changes. 
The result of the inner force and the outer in- 
fluences, working together, complicates the prob- 
lems to such an extent that the pure inductive 
methods are well-nigh impossible of application. 
Resort is then had to determination by statistical 
methods. Large groups of plants and animals are 
examined for the purpose of noting tendencies 
disclosed in the aggregate, but hidden as regards 
their manifestation in the individual. Here, of 
course, classification is an aid in disclosing simi- 
larities and differences that may suggest hypoth- 
eses to explain certain dominant characteristics. 



284 INDUCTIVE LOGIC 

We may, moreover, have merely permanent ef- 
fects presented in perception, the cause having 
ceased to act long since. Thus in geology we have 
facts that have been caused, it is true, but the 
causes can be discerned only as manifested in 
the effects, and, therefore, they can be determined 
only by the method of hypothesis, which may 
lead to verification or not, as the case may be. 
Again, certain sciences may suggest problems 
which concern the explanation or significance, 
not of particular phenomena within the sphere 
of that science, but rather the interpretation of the 
whole body of phenomena which the science in 
question comprehends. The problem is not solved, 
therefore, by any attempt in the way of analysis 
by experiment, but rather in the way of synthesis 
through hypothesis ; that is, the ideal construction 
of a whole which will unify and account for all 
facts, or, in other words, to discern the system 
which underlies and co-ordinates the various par- 
ticular manifestations. This is seen especially 
illustrated in the problems which geology and bi- 
ology present concerning the interpretation of their 
respective phenomena regarded in the light of 
their totality. Astronomy also presents a mass 
of seemingly chaotic phenomena, and yet the aim 
of this science is to reduce them all to some one 
self-consistent system. 

For instance, Mr. Spencer remarks concerning the 
geologist : " He does not take for his problem only 
those irregularities of the earth's crust that are 
worked by denudation; or only those which igneous 



INDUCTIVE METHODS AND THE SCIENCES 285 

action causes. He does not seek simply to under- 
stand how sedimentary strata were formed ; or how 
faults were produced ; or how moraines originated ; 
or how the beds of Alpine lakes were scooped out. 
But taking into account all agencies co-operating 
in endless and ever-varying combinations, he aims 
to interpret the entire structure of the earth's crust. 
If he studies separately the action of rain, rivers, 
glaciers, icebergs, tides, waves, volcanoes, earth- 
quakes, etc., he does so that he may be better 
able to comprehend their joint actions as factors 
in geological phenomena; the object of his science 
being to generalize these phenomena in all their 
involved connections as parts of one whole." Mr. 
Spencer also describes the nature of biology in 
much the same way. " In like manner biology 
is the elaboration of a complete theory of life 
in each and all of its involved manifestations. If 
different aspects of its phenomena are investi- 
gated apart, if one observer busies himself in 
classing organisms, another in dissecting them, 
another in ascertaining their chemical composi- 
tions, another in studying functions, another in 
tracing laws of modification, — they are all con- 
sciously or unconsciously helping to work out 
a solution of vital phenomena in their entirety, 
both as displayed by individual organisms and 
by organisms at large." ' 

Mr. Spencer makes the distinction between in- 
vestigation of particular causal relations on the 
one hand, and, on the other, the interpretation of 

1 Spencer, Classification of the Sciences, pp. 19, 20. 



286 INDUCTIVE LOGIC 

the total phenomena of a science as the basis 
of classification of the sciences. He divides the 
sciences into those which treat of the forms in 
which phenomena are known, snch as the Abstract 
Sciences of mathematics and logic (i.e. formal 
logic) ; and those which treat of the phenomena 
themselves or the Concrete Sciences. The latter 
redivide into the Abstract Concrete Sciences, so 
called, because the specific elements of the con- 
crete phenomena are abstracted from the phe- 
nomena, considered as a whole, and so determined 
as causal laws, relative to particular references 
within the whole body of phenomena which the 
science comprehends; these are such sciences as 
mechanics, physics, chemistry, etc. : the second is 
that of the Concrete Sciences simply, which re- 
gard phenomena in their totalities, as above de- 
scribed. A difference of method is here indicated. 
The Abstract Concrete Series are to be investigated 
analytically, that is, by experiment principally, 
with a view of exhibiting complex phenomena 
in their simplest terms. The simple Concrete 
Sciences are to be treated synthetically, that is, 
by the framing of an hypothesis that will com- 
prehend all particular phenomena in one co-ordi- 
nated whole. 

The division of Herbert Spencer can only be 
accepted in a general way as indicating pre- 
dominant characteristics of the two kinds of sci- 
ences. It will not do to lay down hard and fast 
lines here, for every science presents two kinds 
of problems ; the first, to determine particular 



INDUCTIVE METHODS AND THE SCIENCES 287 

causal relations ; the second, to co-ordinate all snch 
relations into a self-consistent system which will 
unify all separate and individual instances. For 
instance, take the phenomena of light in physics. 
Particular problems as regards intensity, velocity, 
composition of light, etc., present themselves ; 
then an underlying problem, How explain all 
the phenomena of light upon some one single 
basis regarding the essential nature of light. 
Hence arose the emission and undulatory theories 
of light, and all phenomena bearing upon the 
theory were marshalled in support of one and 
of the other, until the conflict was conclusively 
decided. And again, the theory of light, the 
theory of electricity, the theory of heat, etc., 
suggest still another problem, How unify all the 
separate theories in one all-comprehensive theory 
to which the separate phenomena may be alike 
referred. Thus every science presents particular 
problems, and a general problem as well. And 
herein lies a suggestion that all investigators in 
any branch of science would do well to bear in 
mind. Specialization in any one line of particular 
problems should always lead to a consideration 
of the relations of these particular problems to the 
general system of which they are parts. Special- 
ization that does not thus supply its own corrective 
by the natural insistence of the mind to interpret 
the particular in the light of more general laws, 
tends to narrowness of mind and barren results. 

II. In reference to method in the sciences it 
must be observed also that in certain phenomena 



288 INDUCTIVE LOGIC 

the simple theory, which regards the causal con- 
nection as a transfer of energy according to the 
doctrine of the conservation of energy, is further 
complicated by certain variations and modifications 
of the energy in the process of transference. When, 
for instance, a billiard-ball strikes another, and the 
second ball, by virtue of the impact, receives the 
energy of the initial moving ball transferred to it, 
the problem is simplified by the fact that the motion 
of the first is easily traceable in the second, being 
a transfer of energy which manifests itself in the 
same manner in the two cases. However, the prob- 
lem is complicated at once when in chemistry, for 
instance, the two combining elements form a third 
in which the characteristic features of the former 
are wholly lost in the new form. Here is likewise 
a transfer of energy, which may have mechanical 
equivalents, it is true, and yet so radical a change of 
form accompanies the transfer that it complicates 
the problems which arise in this science. We have 
seen how the combined inducto-deductive method 
often predicts events and the nature of phenomena 
not yet observed. And yet this becomes most dif- 
ficult whenever transfer of energy is accompanied 
by a change in the peculiarities of its manifestation 
as well. Knowledge of the nature of two elements, 
and all their separate characteristics, will not be 
sufficient data for any prediction as to the nature 
of the compound. Thus chemistry confronts a 
natural difficulty as regards method, which does not 
affect physical science generally. 

Another difficulty appears in psychology, for here 



INDUCTIVE METHODS AND THE SCIENCES 289 

stimuli from the outer world, expressed in terms of 
physical energy and quantitatively determined, pro- 
duce psychical reactions, that cannot be expressed 
in physical terms. And, on the other hand, proc- 
esses of ideation produce muscular activities, that 
may be estimated in physical terms. It has been 
urged that here the theory of conservation of energy 
breaks down, that the transferred energy is wholly 
accounted for by the nerve and brain modifications, 
and that the psychical accompaniments are wholly 
unaccounted for upon this basis. They stand out 
as unexplored remainders. 

This objection is met in two ways. One is 
that the physical and psychical are, as it were, 
two closed circles, and while simultaneous in their 
functioning do not mutually interact. This is 
the theory of the so-called " psychophysical paral- 
lelism." It necessitates metaphysical explanations 
and postulates that seem to complicate rather than 
simplify the difficulties. The second is the more 
reasonable, that psychical activity may be radically 
different from physical and yet the two capable of 
reacting upon each other, so as to liberate the 
potential activities in either sphere, and thus ini- 
tiate a series of causally connected phenomena. 
Such a theory is buttressed by substantial analogies 
in the physical sphere itself; namely, that in many 
phenomena the impinging force is so modified, by 
the reaction due to the nature of the substance acted 
upon, as to lose, to all observation at least, its orig- 
inal characteristic features. For instance, friction 
passes over into electricity because of the nature of 



290 INDUCTIVE LOGIC 

the substance that is rubbed ; thunder sours cream, 
and thus sound vibrations cause effects wholly 
incongruous to them. 

These illustrations might be multiplied through 
all the realm of physical science. They are so 
many as to prepare us for realizing the possibility, 
at least, that physical excitations may produce 
psychical phenomena in the sense that the outer 
stimulus calls into activity psychical energies, that 
thus stirred, manifest themselves according to the 
forms of their own nature, rather than the forms 
of the physical phenomena exciting them. Upon 
such a theory we may proceed, by observation and 
experiment, to measure duration, intensity, etc., of 
mental reactions responding to external stimuli. 
As regards the method here employed, the series is 
considered as one and complete, so that physical 
excitations are traced, as it were, through an un- 
broken causal chain to their psychical effects, and 
vice versa. On the theory of two closed circles, it 
is difficult to indicate a logical method of experi- 
mental inquiry, unless it be further postulated that 
activities in the one, according to its kind, may 
induce modifications of the other according to its 
kind. This reservation is generally insisted upon. 

III. It sometimes happens that the phenomena 
of one science are to be interpreted in the light of 
the results of another science. Thus the laws of 
one science become guiding principles in investi- 
gating the causal relations existing in another 
sphere. This can only be done when there is some 
similarity between the phenomena of the two sci- 



INDUCTIVE ]\IETHODS AND THE SCIENCES 291 

ences. This method is especially illustrated in his- 
torical explanation. The problem presents a mass 
of events that must be co-ordinated in a system 
wherein their several causal relations will be ex- 
hibited. And not merely must detached epochs be 
proved causally interrelated as regards the events 
occurring in them, but here, also, the special prob- 
lems give rise to a general problem, to discover in 
the whole the philosophy of history, and to deter- 
mine the several historical tendencies in one system 
whose characteristic features will reveal the fact that 
" through the ages one increasing purpose runs." 

To solve the special and the general problems of 
history, recourse is had to an analysis of events on 
the basis of well-established psychological results. 
The phenomena of history are substantially the 
activities of man, both in his individual and col- 
lective capacities. Events being given, an hypothe- 
sis concerning the motives, and ends which actuated 
them, is framed upon the supposition that men ordi- 
narily are impelled by similar motives under similar 
circumstances, in order to achieve similar ends. 
Here the analogies drawn between men of the 
present and men of the past, or between men mov- 
ing in the ordinary routine of every -day life and 
men whose acts may be epoch-making, furnish a 
basis for historical interpretation. We say that 
a series of events, perhaps of a very complicated 
nature, can be explained only by an hypothesis that 
a well-defined purpose and a strong determined will 
were fashioning them and moving through them to 
an end that was in the chief actor's mind from the 



292 INDUCTIVE LOGIC 

beginning. And so the rise of social habits, cus- 
toms, traditions, laws, the religion, the government, 
and national institutions of a people have an origin in 
psychical and not physical elements, a deeper under- 
standing of whose nature and all that it necessitates 
tends to a clearer elucidation of the problems therein 
presented. The knowledge of man, the microcosm, 
is a guiding thread amid the bewildering mazes of 
the macrocosm. It is possible, of course, for the 
imagination of the historian to lead him to wander 
far afield, and invent fanciful motives, purposes, 
public policies, etc., to explain given events. How- 
ever, here, as in the physical and other sciences, the 
hypotheses framed must meet the general require- 
ments and conditions of a valid hypothesis. 

IV. There has been a growing tendency in sciences 
regarded as solely or largely deductive, to correct 
and supplement the traditional method and results 
by a more searching inductive inquiry. This is 
especially true of political economy. The deductive 
method proceeded to build up a body of doctrine 
composed of inferences necessitated by a few fun- 
damental premises. The premises were such as 
the following: The principal motive of action 
is self-interest; the earth, as man's great supply- 
house, is limited in extent and productivity; the 
physical and psychological tendencies of man lead 
him to multiply his own species with a rapid- 
ity which, if not counteracted by obstacles, would 
bring about an unlimited increase of population. 
All economic laws were thus deduced from some 
such fundamental propositions as these. The re- 



INDUCTIVE METHODS AND THE SCIENCES 293 

suits of this deductive method, however, have 
been brought to the bar of another method for 
searching examination and judicial sentence. In 
1848 Hildebrand, and Knies in 1853, with Roscher 
in 1854, set forth the principles of the historical 
school of political economy. They held that an 
inductive inquiry must be started in order to 
estimate the physical, ethnical, and historical con- 
ditions of a nation and its stage of civilization. 
These forces, correctly assessed, will give the eco- 
nomic conditions of a particular period of history, 
or of a particular nation. This is not the place to 
criticise the tenets of this school, but merely to 
point out the fact that its influence has been potent 
in correcting and supplementing the results ob- 
tained in a purely deductive manner. 

Deduction may give the joint effect of universal 
psychological impulses, operative under certain nat- 
ural conditions of environment, etc., provided no 
disturbing force is present. But the question here 
is not whether a certain cause, if acting alone, will 
produce a certain effect ; but whether counteracting 
causes will be present, or modifying causes, as the 
case may be. To estimate the results of collocations 
and not simple causes becomes, as we have seen, a 
complex problem. For its solution recourse must 
be had largely to statistical methods whereby large 
aggregates reveal tendencies that are actual and not 
theoretical merely. 

In a similar way, the historical school of juris- 
prudence, associated with Savigny, has influenced 
the so-called philosophical school in demonstrating 



294 INDUCTIVE LOGIC 

that results theoretically determined by deduction 
are constantly modified by the real conditions and 
limitations of each particular nation's life. The 
influence of this school is indicated by a significant 
fact, that when Hegel wrote his theory of law 
(Rechtslehre) he paid more regard to the historical 
formation of states than did the earlier theorists 
of natural law. 1 

Again, another illustration of the growing prev- 
alency of inductive method is found in the mod- 
ern psychological method. The sole method was 
considered from time immemorial to be that of 
introspection. Its results, however, were meagre; 
the method itself was indefinite and lacked cer- 
tainty and uniformity. Inductive inquiry, there- 
fore, proceeded by its own methods to secure and 
interpret material in other and various fields. As 
Professor Ladd says: "The method of psycholog- 
ical science is peculiarly introspective and analytic 
of the envisaged phenomena called states of con- 
sciousness. But it is far broader and more effective 
than it could be if it were merely introspective. 
It pushes its analysis of the genesis of the phe- 
nomena as far back as possible, by the use of 
experimental methods, and methods of external 
observation applied to the whole process of mental 
evolution (study of infants, of primitive man, and 
of the lower animals, — - evolutionary and compara- 
tive psychology). It interprets the psychological 
life of the individual mind in the light of knowl- 
edge gathered concerning the psychical development 

i Bluntschli, The Theory of the State, p. 69. 



INDUCTIVE METHODS AND THE SCIENCES 295 

of the race (the psychological study of literature, 
society, art, religion, etc.). It lays peculiar empha- 
sis upon abnormal and pathological phenomena of 
the nervous and mental life (psychiatry, hypnotism, 
phenomena of insanity and of the criminal classes, 
etc.). It takes account of the rise and fall of par- 
ticular forms of psychological theory (the history 
of psychology). It strives to transcend experience 
by hypothetical principles of explanation. But in 
the employment of all these methods this science 
differs in no important respect from the sciences 
which deal wholly with physical phenomena. It 
is only the use of introspection for the possession, 
and, to some extent at least, for the analysis, of 
its objects, which makes psychology, as respects 
its method, different from the other sciences." 1 

In the above, we see that inductive inquiry lays all 
possible fields of research under tribute to the one 
end of explaining and correlating psychical phenom- 
ena. The systems of ethics also, which are founded 
upon an a priori basis, are becoming more indebted 
to empirical investigations which have given a richer 
content to the strictly formal ethic. Advanced 
psychological research, the study of race character- 
istics, tribal customs, habits, law, religion, etc., the 
indications of moral progress, — all give material 
which, if interpreted by right hypotheses, will 
throw light upon the theory of ethical principles 
regarded merely from a speculative point of view. 
We may conclude, therefore, that the inductive 
method and the deductive are not mutually exclu- 
1 Ladd, Introduction to Philosophy, p. 116. 



296 INDUCTIVE LOGIC 

sive processes. They may be so combined as mu- 
tually to strengthen one another. What Bluntschli 
says of jurisprudence may be applied equally as 
well to all sciences that claim some a priori basis : 
"The old strife between the philosophical and 
historical schools in Germany has altogether ceased. 
Peace was made as early as 1840. Since then it is 
recognized on all sides that the experiences and 
phenomena of history must be illumined with the 
light of ideas, and that speculation is childish if it 
does not consider the real conditions of the nation's 
life." 1 

It will be seen how important a factor historical 
data becomes, in all the sciences that deal with 
human volition and activities. Whatever hypoth- 
esis may be framed, it must correspond to these data, 
because they represent actual conditions that must 
be co-ordinated in a self-consistent system, and their 
nature and relations satisfactorily interpreted. 

1 Bluntschli, The Theory of the State, p. 70. 



CHAPTER XIX 

Historical Sketch of Induction 

Socrates (470-399 B.C.). — We find the beginnings 
of inductive inquiry in the Socratic or maieutic 
method, that art of mental midwifery by which 
conceptions were to be delivered from the mass of 
individual experiences and opinions in which they 
lie concealed. The Socratic procedure in the forma- 
tion of conceptions is to question every particular 
view, and estimate it by bringing together analogous 
cases, and discovering their natural connections, so 
as to explicate the general notion which it contains, 
and thus proceed from comparison of particulars to 
the framing of general propositions. Socrates' gen- 
eralizations were many of them hasty, and in his 
desire to formulate a general conception he over- 
looked exceptions and minimized difficulties, but in 
his method there were the germs of truly scientific 
procedure. The sphere of his method was, however, 
limited, as he applied it only to the illumination of 
ethical controversies. 

Plato (427-347 B.C.). — Plato enriched the Socratic 
method of induction by removing its limitation to 
ethical inquiry. Plato was especially concerned 
with investigating the relations of his " ideas " to 
each other, and this led to the apprehension of the 
297 



298 INDUCTIVE LOGIC 

logical relations between conceptions, especially as 
regards their subordination and co-ordination. This 
forms a basis for classification, — Plato's division of 
class-concepts or logical genera into their species is a 
prominent feature of his method. He also suggests 
the hypothetical method of treating the relations of 
concepts ; namely, to examine a tentatively proposed 
conception by developing all the possible conse- 
quences that would follow from its union with known 
conceptions. This is in keeping with the inducto- 
deductive method of Mill and the modern logicians. 
Aristotle (384-322 b.c). — Aristotle's name is es- 
pecially, and it may be said almost exclusively, 
associated with deductive logic and syllogistic 
reasoning. Although he did not develop fully 
the inductive logic, he nevertheless did not ignore 
it, in some of its essential features at least. He 
acknowledged the necessity of investigating the 
starting-point of deduction, namely, the ultimate 
grounds of proof, and of the principles of explana- 
tion. This process he called dialectic. It is a 
double process that proceeds from the particulars 
given in perception, and from the ideas current in 
customary opinion, to discover the general, and 
then from the general to deduce the particular, 
which is thereby verified in the process. The 
former procedure is the reverse of the deductive, 
and is epagogic or inductive. Induction, according 
to him, is a syllogism in which the inference that 
the major belongs to the middle, is mediated 
through the minor directly; and not indirectly 
through the middle. Thus, to use Aristotle's illus- 



HISTORICAL SKETCH OF INDUCTION 299 

tration, the investigation of the connection between 
the absence of gall in animals and longevity in a 
number of instances, as in man, horse, mule, etc., 
may disclose their coexistence. 1 They are then 
united directly without mediation of a middle term. 
If we had given the universal proposition to start 
with, Whatever animal has no gall is long-lived, 
and the minor premise that man, horse, mule, etc., 
are animals having no gall, then the conclusion 
would follow, therefore they are long-lived. This 
is the deductive syllogism. The inductive method, 
on the other hand, starts from particular observa- 
tion that the horse which has no gall is long-lived, 
so also the mule, so also man, etc. ; therefore, 
without any middle term, a coexistence is taken 
as equivalent to a causal relation between these 
attributes, and the inference is drawn that all ani- 
mals having no gall are long-lived. Such an infer- 
ence is valid syllogistically, however, only on the 
assumption that the instances examined comprise 
the whole class having the attributes under investi- 
gation. This inductive syllogism, therefore, ex- 
presses inferences only of complete enumeration. 
The form of such a syllogism is as follows : — 

Let S = minor term, 

P= major term, 

M — middle term. 
This, that, and the other S is P. 
This, that, and the other S is all M. 
.-. All M is P. 

1 Aristotle, Prior Analytics, II. xxiii. 



300 INDUCTIVE LOGIC 

Here it will be observed that the particular in- 
stances comprising the minor term S, when summed 
up, equal the middle term. There is no inference 
in this if we have regard to the strict sense in 
which the word is used. Aristotle, indeed, consid- 
ered the only scientific induction to be the so-called 
perfect induction, and says that to generalize many 
experiences of the same kind is admissible only 
when there is no contrary case. The thought that 
causal connection enables us to generalize is stated 
by Aristotle, but, as Ueberweg says, it "does not 
attain to a fundamental significance in his logical 
theory." 1 

The Precursors of Bacon. — The revolt against 
the scholasticism of the Middle Ages and the 
fetters of the Aristotelian logic was many-voiced, 
culminating, however, as regards the emphasis 
placed upon induction as a scientific method, in the 
works of Francis Bacon. 

Foremost among the early champions of induc- 
tive inquiry we find Roger Bacon, born in 1214, 
a Franciscan monk, yet devoted heart and mind 
to the cause of science. His Opus Majus was 
published first in 1733 by Dr. S. Jebb, principally 
from a manuscript in the library of Trinity College, 
Dublin. This work is characterized by a spirit of 
protest against authority in general, and that of 
Aristotle and his logic especially. He recom- 
mends mathematics and experiment as the two 
great instruments of scientific investigation. In 
this particular it is interesting to note his antici- 

1 Ueberweg, Logic, p. 479. 



HISTORICAL SKETCH OF INDUCTION 301 

pation of the modern mathematico-physical modes 
of scientific inquiry. The following quotation will 
give an indication of his spirit and aims : — 

" Experimental science, the sole mistress of spec- 
ulative sciences, has three great prerogatives among 
other parts of knowledge: First, she tests by ex- 
periment the noblest conclusions of all other sci- 
ences ; next, she discovers, respecting the notions 
which other sciences deal with, magnificent truths 
to which these sciences of themselves can by no 
means attain ; her third dignity is, that she by her 
own power, and without respect of other sciences, 
investigates the secrets of nature." * 

Leonardo da Vinci (1452-1519). — Leonardo com- 
bined in one personality many brilliant talents, be- 
ing eminent as sculptor, painter, architect, engineer, 
astronomer, and natural philosopher. His works, 
unpublished, exist in manuscripts in the library of 
the Institute at Paris. He expresses himself very 
clearly and emphatically concerning the relation of 
experience to speculation : " Theory is the general ; 
experiments are the soldiers. We must consult ex- 
perience, and vary the circumstances till we have 
drawn from them general rules ; for it is she who 
furnishes true rules. But of what use, you ask, are 
these rules ? I reply, that they direct us in the 
researches of nature and the operations of art. 
They prevent our imposing upon ourselves and 
others, by promising ourselves results which we 
cannot obtain. But see the absurdity of men ! 

1 Whewell, Philosophy of the Inductive Sciences, Vol. II. 
p. 333. 



302 INDUCTIVE LOGIC 

They turn up their noses at a man who prefers to 
learn from nature herself rather than from authors 
who are only her clerks." 1 This latter remark is 
similar in its reference to the epithet of Galileo, 
applied to men whose knowledge comes wholly 
from books and not from observation; namely, 
" paper philosophers." 

Bernardinus Telesius (1508-1588). — His work, en- 
titled De Rerum Natura, anticipated, in some degree 
at least, the Novum Organon of Bacon. Bacon 
himself says of him : " We think well concerning 
Telesius, and acknowledge him as a lover of truth, 
a useful contributor to science, an amender of 
some tenets, the first of recent men." Telesius 
set for himself a high aim and purpose, but in 
the application of his method he was not so fortu- 
nate, being dominated in his researches by specu- 
lation rather than the results of experimental 
inquiry. As to his professed method, he announces 
in the title of his De Natura that " the construction 
of the world, the magnitude and nature of the 
bodies contained in it, are not to be investigated by 
reasoning, which was done by the ancients, but are 
to be apprehended by the senses and collected from 
the things themselves." And in the Proem of the 
same work he says in the same strain that " they 
who before us have inquired concerning the con- 
struction of this world, and of the things which it 
contains, seem indeed to have prosecuted their ex- 
amination with protracted vigils and great labor, 

1 Whewell, Philosophy of the Inductive Sciences, Vol. II. 
p. 369. 



HISTORICAL SKETCH OF INDUCTION 303 

but never to have looked at it. For, as it were, 
attempting to rival God in wisdom, and venturing 
to seek for the principles and causes of the world 
by the light of their own reason, and thinking they 
had found what they had only invented, they made 
an arbitrary world of their own. We then, not 
relying on ourselves, and of a duller intellect than 
they, propose to ourselves to turn our regards to 
the world itself and its parts." 

Following Telesius, and of his school, was Thomas 
Campanella (1568-1639). He was a contemporary 
of Bacon, and, under the influence of Telesius, early 
conceived the idea of an inductive method of re- 
search. At the age of twenty-two, he published a 
work whose character may be judged by its title, — 
" Thomas Campanella's Philosophy demonstrated 
to the senses, against those who have philosophized 
in an arbitrary and dogmatical manner, not taking 
nature for their guide ; in which the errors of Aris- 
totle and his followers are refuted from their own 
assertions and the laws of nature ; and all the 
imaginations feigned in the place of nature by the 
Peripatetics are altogether rejected ; with a true 
defence of Bernardin Telesius of Cosenza, the 
greatest of philosophers ; confirmed by the opin- 
ions of the ancients, here elucidated and defended, 
especially those of the Platonists." 

The ideas of Bacon, with their impetus to the 
inductive method of research, were not only antici- 
pated by writers of books ; but actual discoveries 
by zealous investigators were turning the attention 
of the thinking world to nature and her secrets. 



304 INDUCTIVE LOGIC 

There was an illustrious line of pioneers in this 
undiscovered country. There was Andrew Caesal- 
pinus (1520-1603), the founder of the science of 
botany ; and earlier, Copernicus (1473-1543), ad- 
vancing his heliocentric theory ; and Gilbert (1540- 
1603), the court physician of Elizabeth and James, 
conducting with untiring perseverance his investi- 
gations of the nature of magnetism and electricity. 
Kepler, born ten years after Bacon, 1571, and 
Galileo, born in 1564, and their contemporary, 
Tycho Brahe, born in 1546, formed a triumvirate 
of scientific power and brilliancy, made resplendent 
by the glory of the heavens itself. It must be 
remembered, too, that at this time a new world had 
been discovered across the seas; the recent inven- 
tions of gunpowder, of the mariner's compass, and 
of the art of printing, all tended to stimulate the 
thought of the world, and usher in a new epoch in 
the history of civilization. 

Francis Bacon (1561-1626). — Bacon's inductive 
system is given, for the most part, in the Novum 
Organon. The title of this work was in itself a 
protest against Aristotle and his logic, implying 
that Aristotle's Organon was now out of date and 
was to be superseded by the new. Bacon insists that 
all knowledge of nature has for its end the disclos- 
ing of the causes of things. According to the Aris- 
totelian scheme, causes are formal, material, efficient, 
or final. Bacon is only concerned with the formal 
causes. For, he says, all events have their ground 
in the " forms " of things. By the form of a 
thing, he meant its essential nature. Where he 



HISTORICAL SKETCH OF INDUCTION 305 

uses the form we may well supply the word, 
law. To discover the forms of phenomena, it is 
necessary, according to Bacon, to collect as many in- 
stances as possible in which the phenomenon under 
investigation appears ; together they form a tabula 
prcesentice. In like manner, the instances in which 
the phenomenon is lacking are grouped in a tabula 
absentice; and a third group must be formed, — a 
tabula, graduum in which the variations of intensity 
in the phenomena are compared with the varying 
intensity of other phenomena. The problem is 
then to be solved by a process of exclusion (exclu- 
sio) ; that is, the rejection or exclusion of the several 
qualities which are not found in some instance 
where the given quality is present, or are found in 
some instance where the given quality is absent, 
or are found to increase in some instance where the 
given quality decreases, or to decrease when the 
given quality increases. By this process an indica- 
tion will be given by which an hypothesis may be 
framed, and finally verified by subsequent observa- 
tion and experiment. In the sketch of this method 
it will be seen that his three tables of instances 
closely resemble the methods of agreement, of 
difference, and of concomitant variations. They, 
however, lack the precision of the later formula- 
tion of these methods. There is no hint at a syste- 
matic selection and variation of the instances ; and 
no requirement, as in the method of difference, 
that two instances shall be so experimentally de- 
termined that they will agree in every point save 
the given phenomenon, which is present in the one 
x 



306 INDUCTIVE LOGIC 



and absent from the other. Bacon, however, made 
a substantial contribution to the method of induc- 
tion in general, in insisting upon the examination 
of instances themselves, and in ascending from 
them quite gradually the scale of the more general 
up to the most general, and in this he entered a 
vigorous protest against hasty generalization. 

As to the manner of certifying the hypothesis 
formed after the process of collecting and sifting 
instances, Bacon has no recourse to deduction 
based upon the hypothesis and consequent verifica- 
tion. He seems to despise mathematical method 
s an ally of inductive inquiry ; and, therefore, has 
o place in his scheme for the prediction of new 
phenomena by means of calculation. Of his nine 
divisions of aids to induction, he completed only 
the first, — Prerogative Instances. Of the instances 
which he enumerates, twenty-seven in all, only a 
few have any bearing directly upon the inductive 
method proper. Two sets of these instances may 
be considered as a crude statement of the methods 
of agreement and difference ; the Solitary Instances, 
which either exhibit a phenomenon without any of 
its usual accompaniments or which agree in every- 
thing except some particular phenomenon, and 
Migratory Instances, where qualities are produced 
in bodies by evident causes, as, for instance, the 
producing of whiteness by pounding glass, also by 
stirring water into froth. These instances, how- 
ever, as exhibited by Bacon, lack precision and the 
possibilities of accurate determination of causal con- 
nections. The only other group of instances hav- 



HISTORICAL SKETCH OF INDUCTION 307 

ing special inductive significance is that of the In- 
stant ia Cruets; as before mentioned, such instances 
are valuable in deciding between rival hypotheses. 
With all the deficiencies of Bacon's method, how- 
ever, his service to the thinking world is indispu- 
table, in emphasizing the need of investigating 
phenomena themselves as a corrective of fanciful 
speculations, and in his vigorous warnings against 
prejudice, against intellectual indolence, against 
subjection of the mind to the trammels of author- 
ity, and against over-hasty generalizations. 

Locke (1632-1704). — Locke applied the method 
of Bacon to the objects of inner experience. He 
declared that the data of all knowledge come from 
sensation, or sense-perception, and from reflection, 
and that there are no "innate ideas," and there- 
fore no starting-point for a priori speculations. 
The method that had been found useful in actual 
discoveries, such as those of Newton, Kepler, and 
others, Locke insisted would prove productive also 
of rich results in the intellectual sphere. 

Isaac Newton (1642-1727). — Scientific method 
was gradually formulating itself in the actual pur- 
suits of scientific investigation, — not thought out 
as much as worked out, and its efficiency tested and 
confirmed by results. Newton gives form to that 
which was a result of many experiments, and of a 
mass of various experiences, in his Rules of Phi- 
losophizing (Reguhe Philosophandi) prefixed to the 
Principia. 

These rules are as follows : — 

1. The first rule is twofold : — 



308 INDUCTIVE LOGIC 

a. " Only real causes are to be admitted in ex- 
planation of phenomena." 

b. " No more causes are to be admitted than such 
as suffice to explain the phenomena." 

2. " In as far as possible, the same causes are to 
be assigned for the same kind of natural effects." 

3. "Qualities that can neither be increased nor 
diminished in intensity, and that obtain in all 
bodies accessible to experiment, must be considered 
qualities of all bodies whatsoever." 

4. "In philosophical experiment, propositions 
collected from phenomena by induction are to 
be held, notwithstanding contrary hypotheses, as 
either exactly or approximately true, until other 
phenomena occur whereby they are either rendered 
more exact or are proved liable to exceptions." 

Newton's celebrated saying, "Hypotheses non 
fingo," was originally a protest against the sup- 
position of the existence of occult or imaginary 
causes to explain phenomena, notably the Car- 
tesian explanation of the celestial movements by 
vortices. Hypotheses of a different nature, and 
rationally grounded of course, did not fall under 
Newton's reprehension. 

Sir John Herschel (1792-1871). — Herschel's Dis- 
course on the Study of Natural Philosophy was pub- 
lished in 1832. John Stuart Mill reviewed this book 
in the Examiner and was evidently impressed and 
influenced by it. Herschel's design was to make 
the methods of science more explicit. These are 
contained in nine " propositions readily applicable 
to particular cases, or rules of philosophizing." 



HISTORICAL SKETCH OF INDUCTION 309 

Of these propositions, the second, seventh, eighth, 
and ninth present substantially the experimental 
methods as afterwards more precisely formulated 
by Mill. These methods, however, he regards sim- 
ply as means to discovery, and not methods of 
proof. Of the remaining propositions, the first 
is a more precise statement of Bacon's principle 
of exclusion, and is the foundation of the joint 
method of agreement and difference. The third 
proposition is that " we are not to deny the exist- 
ence of a cause in favor of which we have a 
unanimous agreement of strong analogies, though 
it may not be apparent how such a cause can pro- 
duce the effect, or even though it may be difficult 
to conceive its existence under the circumstances 
of the case." The fourth is that "contrary or 
opposing facts are equally instructive for the dis- 
covery of causes with favorable ones." The fifth 
recommends the " tabulation of facts in the order 
of intensity in which some peculiar quality sub- 
sists." The sixth rule insists upon the investi- 
gator keeping prominently in mind the possibility 
that '• counteracting or modifying causes may sub- 
sist unperceived," and that this fact may be the 
means of explaining many apparent exceptions. 

Herschel also emphasizes the necessity of com- 
bining induction and deduction in complicated in- 
quiries; and, further, he explains the nature of 
empirical laws, as also the nature and tests of 
hypotheses. \We can now see that the body of in- 
ductive principles begins at length to assume final 
form and proportion. 



310 INDUCTIVE LOGIC 

Wliewell (1795-1866). — Dr. Whewell published 
his Philoso2)hy of the Inductive Sciences in 1840, 
containing his system of induction. His method in- 
volves two principal processes, — the colligation of 
facts and the explication of conceptions. The inves- 
tigator is to gather all the facts at his disposal, and 
upon them he is to superinduce a conception which 
will unify them, or colligate them. He says these 
conceptions are supplied by the mind, while facts are 
supplied by the sense. This, however, is a distinc- 
tion that separates so widely the spheres of the 
particular facts, and the general conceptions, that 
upon such a basis a union of the two as explaining 
one by the other would be artificial and with no 
corresponding bond of reality. The colligating 
conception does not exist in the mind before or 
apart from its existence in fact. The attempt to 
fit facts to ready-made conceptions is of the nature 
of guess-work. Kepler's nineteen guesses regarding 
planetary orbits is an instance of attempting to 
superinduce conceptions upon a mass of facts. It 
is not a truly scientific or logical procedure, and 
the great danger of applying it lies in the fact 
that the mind all too readily tends to mould facts 
into the forms of prior conceptions. 

"The Methods employed in the Formation of 
Science," the title of his concluding chapter, are 
three, as follows : Methods of Observation, Meth- 
ods of Obtaining Clear Ideas, and Methods of 
Induction. The last principally concerns our 
present purposes. The methods of induction are 
methods of discovery rather than proof, save the 



HISTORICAL SKETCH OF INDUCTION 311 

last, which is one of the experimental methods. 
They are the method of curves to express graphi- 
cally the graduated results of several observations ; 
the method of means, and the method of least 
squares, both designed to eliminate accidental ac- 
companiments of constant causes by striking an 
average of several observations ; and the method of 
residues. Whewell's method may be characterized 
in brief as a method of discovery rather than proof. 
John Stuart Mill (1806-1873). — Mill's Logic, 
published in 1843, was essentially a method of 
proof rather than a method of discovery. His aim 
in formulating the methods in vogue in experimen- 
tal science, was to discover the precise modes of 
their operation in order to apply the same in inves- 
tigating the various mental, moral, social, and polit- 
ical phenomena. Bacon in the Novum Organon had 
asserted that this inductive method was applicable 
to the intellectual and moral sciences. This was no 
doubt suggestive to Mill, as it had been to Locke. 
Whately's Logic, published in 1827, influenced Mill, 
and was the means of turning his attention to logi- 
cal studies. Whately's book was reviewed by Mill, 
when only twenty-one, in the Westminster Review. 
The revival in logical interest at this time and 
the departure from scholastic traditions have been 
traced to the influence of Edward Copleston, tutor 
at Oxford, and afterwards Bishop of Llandaff. 
Whately's work represented the first-fruits, and 
Mill's the richer and riper product of this revival 
of logic. It is a matter of more than passing 
interest to note that one of Whately's most active 



312 INDUCTIVE LOGIC 

collaborators in the work was John Henry Newman, 
so that, as Professor Minto says, " the common room 
of Oriel, which Mr. Froude describes as the centre 
from which emanated the High Church Movement, 
may also be said to have been the centre from which 
emanated the movement that culminated in the rev- 
olution of logic." 

Mill's special office as regards induction consists 
in his crystallizing the principles and practices of the 
scientific investigators who had caught and reflected 
the spirit of modern research. The formulated meth- 
ods of inductive logic, substantially as given by Mill, 
have become the recognized methods of all investi- 
gation that is actuated by a scholarly spirit and a 
scientific habit, j Mill's contributions to the induc- 
tive logic have been so largely drawn from and so 
frequently referred to in the composition of this 
book, as to need no further comment here. The 
works of the more recent writers, as Lotze, Sigwart, 
Bosanquet, Jevons, Venn, etc., have also been noticed 
in the body of the text. Their work is largely crit- 
ical, and no distinct inductive system is especially 
associated with any of their names. 



CHAPTER XX 

Logical Exercises 

In the following examples, indicate the nature 
of the inferences, the methods employed, and the 
character of the results obtained, whether valid 
or invalid, and the reasons for the same. 

1. In all unhealthy countries the greatest risk of 
fever is run by sleeping on shore. Is this owing to 
the state of the body during sleep, or to a greater 
abundance of miasma at such times? It appears 
certain that those who stay on board a vessel, 
though anchored at only a short distance from 
the coast, generally suffer less than those actually 
on shore. — Darwin in Voyage of Naturalist. 

2. That the period of the tide should be acciden- 
tally the same as that of the culmination of the 
moon, that the period of the highest tide should be 
accidentally the same as that of the syzygies, is 
possible in abstracto ; but it is in the highest degree 
improbable ; the far more probable assumption is, 
either that sun and moon produce the tide, or that 
their motion is due to the same grounds as the 
motion of the tide. 

3. In measuring the velocity of sound by experi- 
ments conducted at night with cannon, the results 

313 



314 INDUCTIVE LOGIC 

at one station were never found to agree exactly 
with those at the other. Moreover, it was noticed 
that on the nights when the discordance was great- 
est, a strong wind was blowing nearly from one 
station to the other. 

4. M. Melloni, observing that the maximum 
point of heat is transferred farther and farther 
towards the red end of the spectrum, according 
as the substance of the prism is more and more 
permeable to heat, inferred that a prism of rock- 
salt, which possesses a greater power of transmit- 
ting the calorific rays than any known body, ought 
to throw the point of greatest heat to a consider- 
able distance beyond the visible part of the spec- 
trum ; and his prediction was verified by subsequent 
experiment. 

5. During the middle of the eighteenth century 
Bonnet and Spallanzani discovered that the horns, 
tails, legs, eyes, or even head of some creatures, if 
cut off, would grow again. The tail and legs of a 
salamander were removed and reproduced them- 
selves eight times in succession. By means of a 
number of experiments it has been found that the 
more simple the structure of an animal is, the 
more do its several parts possess a power of inde- 
pendent existence, and that in the more complex 
animals, the derangement of one part much more 
affects the action of the entire organism. 

6. Professor Jevons has observed that economic 
crises have occurred at regular intervals of about ten 
years. This ten-year periodicity, moreover, seems to 
correspond to a similar periodicity of bad harvests ; 



LOGICAL EXERCISES 315 

and the cause of this seems to be a decennial peri- 
odicity in the spots on the sun. 

7. What is the significance of the remark of 
Chevreul, the French scientist : " Every fact is an 
abstraction." 

8. Also of the following remark of M. Espinas : 
" If human activity was incompatible with the order 
of things, the act of boiling an egg would have to be 
regarded as a miracle." 

9. It had long been known that grasshoppers 
and crickets have on their anterior legs two pecul- 
iar, glassy, generally more or less oval, drum-like 
structures; but these were supposed by the older 
entomologists to serve as resonators, and to rein- 
force or intensify the well-known chirping sounds 
which they produce. Johannes Midler was the 
first who suggested that these drums or tympana 
act like the tympanum of our own ears, and that 
they are really the external parts of a true audi- 
tory apparatus. That any animal should have its 
ears in its legs sounds, no doubt, a priori, very 
unlikely, and hence probably the true function of 
this organ was so long unsuspected. — Sir John 
Lubbock. 

10. In simple fracture of the ribs, if the lung 
be punctured by a fragment, the blood effused into 
the pleural cavity, though freely mixed with air, 
undergoes no decomposition. Why air introduced 
into the pleural cavity through a wounded lung 
should have such wholly different effects from that 
entering directly through a wound in the chest was 
to me a complete mystery until I heard of the germ- 



316 INDUCTIVE LOGIC 

theory of putrefaction, when it at once occurred to 
me that it was only natural that air should be fil- 
tered of germs by the air-passages, one of whose 
offices is to arrest inhaled particles of dust and 
prevent them from entering the air-cells. — Pro- 
fessor Lister. 

11. If the lungs be emptied as perfectly as pos- 
sible and a handful of cotton-wool be placed against 
the mouth and nostrils, and you inhale through it, 
it will be found on expiring this air through a glass 
tube that its freedom from floating matter is mani- 
fest. The application of this is obvious ; if a phy- 
sician wishes to hold back from the lungs of his 
patient, or from his own, the germs, or virus by which 
contagious disease is propagated, he will employ a 
cotton-wool respirator. — Professor Tyndall. 

12. In the desert of North Africa, where neither 
trees, brushwood, nor even undulation of the surface 
afford the slightest protection to its foes, a modifi- 
cation of color in animals which shall be assimilated 
to that of the surrounding country is absolutely 
necessary. Hence, without exception, the upper 
plumage of every bird, whether lark, chat, sylvian, 
or sand-grouse, and also the fur of all the smaller 
mammals and the skin of all snakes and lizards, is 
of one uniform isabelline, or sand color. — Wallace. 

13. Darwin, in investigating the difference in 
weight between cross and self fertilized plants, 
found that the six finest crossed plants averaged 
108.16 ounces, whilst the six finest self fertilized 
plants averaged only 23.7 ounces or as 100 to 22. 

14. Bees incessantly visit the flowers of the com- 



LOGICAL EXERCISES 317 

mon broom and these are adapted by a curious mech- 
anism for cross-fertilization. When a bee lights 
on the wing-petals of a young flower, it is slightly 
opened, and the short stamens spring out, which 
rub their pollen against the abdomen of the bee. 
If a rather older flower is visited for the first time 
(or if the bee exerts great force on a younger 
flower), the keel opens along its whole length, and 
the longer as well as the shorter stamens, together 
with the much elongated curved pistil, spring forth 
with violence. The flattened spoon-like extremity 
of the pistil rests for a time on the back of the 
bee, and leaves on it the load of pollen with which 
it is charged. As soon as the bee flies away, the 
pistil instantly curls round, so that the stigmatic 
surface is now upturned and occupies a position, in 
which it would be rubbed against the abdomen of 
another bee visiting the same flower. Thus, when 
the pistil first escapes from the keel, the stigma is 
rubbed against the back of the bee, dusted with 
pollen from the longer stamens, either of the same 
or another flower ; and afterwards against the lower 
surface of the bee, dusted with pollen from the 
shorter stamens, which is often shed a day or two 
before that from the longer stamens. If the visits 
of bees are prevented, and if the flowers are not 
dashed by the wind against any object, the keel 
never opens, so that the stamens and pistil remain 
enclosed. Plants thus protected yield very few 
pods in comparison with those produced by neigh- 
boring uncovered bushes, and sometimes none at 
all. — Darwix. 



318 INDUCTIVE LOGIC 

15. Baron Zach received a letter from Pons, a 
successful finder of comets, complaining that for a 
certain period he had found no comets, though he 
had sought diligently. Zach, a man of much sly 
humor, told him that no spots had been seen on 
the sun for about the same time — which was true 
— and assured him that when the spots came back, 
the comets would come with them. Some time 
after that he got a letter from Pons, who informed 
him, with great satisfaction, that he was quite 
right, that very large spots had appeared on the 
sun, and that he had found a fine comet shortly 
after. — De Morgan's Budget of Paradoxes. 

16. If Tellus winged be, 

The earth a motion round ; 
Then much deceived are they 

Who nere before it found. 
Solomon was the wisest, 

His wit nere this attained ; 
Cease, then, Copernicus, 

Thy hypothesis vain ! 

— Sylvanus Morgan, 1652. 

17. Weather Forecaster Dunn has prepared a 
chart showing the number of deaths from grip in 
New York City during the period from March 22 
to May 16, 1891, establishing the relation between 
the death-rates and weather conditions during the 
grip epidemic of that year. Mr. Dunn has made a 
careful study of records of the disease, and selected 
the epidemic of 1891 as being the time when the 
grip was most pronounced. 



LOGICAL EXERCISES 819 

He has apparently demonstrated that the weather 
is an important factor in the mortality of grip cases. 
He says that humidity or moisture in the air seems 
to be the most important element in causing the 
disease to spread. There is a corresponding in- 
crease of deaths with increasing humidity. 

The fatality is most marked when the humidity 
is at its maximum and there is a sudden fall of the 
temperature. This is shown by the record of April 
21, when the death-rate from grip was the highest 
ever known. During the twenty-four hours of that 
day 250 deaths were reported. On April 1 and 
April 30 the death-rate was also high. These were 
days following a sudden fall in temperature. 

All through the epidemic the charts show an 
increasing death-rate with high or increasing hu- 
midity. The higher the humidity and the more 
sudden the fall in temperature, the greater was the 
number of deaths. When the temperature and the 
humidity dropped at the same time, there was a de- 
crease in the death-rate, as Mr. Dunn points out by 
several examples. He says that the lesson to be 
learned from his chart is that those suffering from 
an incipient attack of the grip should be most 
cautious of the cold, humid days that immediately 
follow the warm, damp ones. 

18. If in a reservoir immersed in water, the air 
be compressed to the extent of ten atmospheres, 
and supposing that now, when the compressed air 
has acquired the temperature of the water, it be 
allowed to act upon a piston loaded by a weight, 
the weight is raised. At the same time the water 



320 INDUCTIVE LOGIC 

becomes cooler, showing that a certain quantity of 
heat had disappeared in producing the mechanical 
effort of raising the weight. 

19. That the feeling of effort is largely, if not 
entirely, of peripheral, rather than central origin, 
appears from such experiments as the following : — 

Hold the finger as if to pull the trigger of a pis- 
tol. Think vigorously of bending the finger, but 
do not bend it. An unmistakable feeling of effort 
results. Repeat the experiment, and notice that 
the breath is involuntarily held, and that there are 
tensions in the other muscles. Repeat the experi- 
ment again, taking care to keep the breathing regu- 
lar and the other muscles passive. Little or no 
feeling of effort will now accompany the imaginary 
bending of the finger. — Ferrier. 

20. As to the nature of petrified shells, Quirini 
conceived that as earthy particles united in the sea 
so as to form the shells of Mollusca, the same crys- 
tallizing process might be effected on the land; and 
that in the latter case, the germs of the animals 
might have been disseminated through the sub- 
stance of the rocks, and afterwards developed by 
virtue of humidity. 

21. Voltaire suggested that the marine shells 
found on the tops of mountains are Eastern species 
dropped from the hats of pilgrims as they returned 
from the Holy Land. 

22. The epicyclical theory of the heavens was 
confirmed by its predicting eclipses of the sun and 
moon, configurations of the planets, and other celes- 
tial phenomena. 



LOGICAL EXERCISES 321 

23. Arfvedson discovered lithia, by perceiving 
an excess of weight in the sulphate produced from 
a small portion of what he considered as magnesia 
present in a mineral he had analyzed. 

24. We see among the nebulae (which are dif- 
fused along the Milky Way) instances of all degrees 
of condensation, from the most loosely diffused 
fluid, to that separation and solidification of parts 
by which suns and satellites and planets are 
formed; and thus we have before us instances of 
systems in all their stages ; as in a forest we see 
trees in every period of growth. — Laplace. 

25. It had been deductively inferred from the 
Copernican theory that the planets, Venus and Mer- 
cury, ought to pass through phases, like the moon, 
and the telescope revealed this to be the case. 

26. Werner, says Sir Charles Lyell, had not 
travelled to distant countries ; he had merely ex- 
plored a small portion of Germany, and conceived, 
and persuaded others to believe, that the whole sur- 
face of our planet, and all the mountain chains in 
the world, were made after the model of his own 
province. 

27. Schemer was a monk ; and on communicating 
to the superior of his order the account of the spots 
on the sun, received the reply : " I have searched 
through Aristotle, and can find nothing of the kind 
mentioned : be assured, therefore, that it is a decep- 
tion of your senses, or of your glasses." 

28. When we are told that a man has become 
deranged from anxiety or grief, we have learned 
very little if we rest content with that. How does 



322 INDUCTIVE LOGIC 

it happen that another man, subjected to an ex- 
actly similar cause of grief, does not go mad ? — ■ 
Maudsley. 

29. It was a general belief at St. Kilda that the 
arrival of a ship gave all the inhabitants colds. Dr. 
John Campbell took pains to ascertain the fact and 
to explain it as the effect of effluvia arising from 
human bodies ; it was discovered, however, that the 
situation of St. Kilda renders a northeast wind in- 
dispensably necessary before a ship can make the 
landing. 

30. Chrysippus maintained that cock-fighting was 
the final cause of cocks, these birds being made by 
Providence in order to inspire us by the example of 
their courage. 

31. Touch in succession various objects on the 
table. A paper-weight, if metallic, is usually cold 
to the touch ; books, paper, and especially a woollen 
table-cover, comparatively warm. Test them by 
means of a thermometer, and there will be little or 
no difference in their temperatures. Why then do 
some feel cold, others warm to the touch? The 
sense of touch does not inform us directly of tem- 
perature, but of the rate at which our finger gains or 
loses heat. As a rule, bodies in a room are colder 
than the hand, and heat always tends to pass from 
a warmer to a colder body. Of a number of bodies, 
all equally colder than the hand, that one will seem 
coldest to the touch, as the metallic, which is able 
most rapidly to convey away heat from the hand. 
— Tait. 

32. One of Joule's experiments concerning the 



LOGICAL EXERCISES 323 

mechanical value of light is as follows : He com- 
pared the heat evolved in the wive conducting a gal- 
vanic current when the wire was ignited by the 
passage of the current, with that evolved when with 
an equal current it was kept cool by immersion in 
water. These experiments showed a small but un- 
mistakable diminution of the heat when light also 
was given out. — Tait. 

33. It is an illusion in psychology and a corrup- 
tion of logic to take the conditions which occasion 
the logical operations of thought for the operations 
themselves. There is only one delusion more des- 
perate still, — to imagine that a complete physical 
theory of the nervous system will explain that 
which is itself the condition of any theory being 
possible at all. — Lotze. 

34. During the retreat of the Ten Thousand a 
cutting north wind blew in the faces of the soldiers ; 
sacrifices were offered to Boreas, and the severity of 
the wind immediately ceased, which seemed a proof 
of the god's causation. 

35. It has been shown by observation that over- 
driven cattle, if killed before recovery from their 
fatigue, become rigid, and putrefy in a surprisingly 
short time. A similar fact has been observed in the 
case of animals hunted to death, cocks killed during 
a fight, and soldiers slain in battle. The contrary 
is remarked when the muscular exercise has not 
been great or excessive. 

36. A correct analysis of lapis lazuli was sus- 
pected to be erroneous because there seemed to be 
nothing in the elements assigned to it, which were 



324 INDUCTIVE LOGIC 

silica, alumina, soda, sulphur, and a trace of iron, to 
account for the brilliant blue color of the stone. 

37. According to the theory that the earth has 
but a thin crust, it is still substantially a liquid 
globe, and therefore, under the attractive influence 
of the sun and moon, it ought to behave like a yield- 
ing liquid. According to Hopkins, Thomson, and 
others, the earth in all its astronomical relations be- 
haves like a rigid solid, — a solid more rigid than a 
solid globe of glass, — and the difference between the 
behavior of a liquid globe and a solid globe could 
easily be detected by astronomical phenomena. — 
Le Conte. 

38. Many years ago I was struck with the fact 
that humblebees, as a general rule, perforate flowers 
only when these grow in large numbers near together. 
In a garden where there were some very large 
beds of Stachys coccinea and of Pentstemon argutus, 
every single flower was perforated ; but I found two 
plants of the former species growing quite separate 
with their petals much scratched, showing that they 
had been frequently visited by bees, and yet not a 
single flower was perforated. I found also a sepa- 
rate plant of the Pentstemon, and saw bees entering 
the mouth of the corolla and not a single flower had 
been perforated. In the following year (1842) I 
visited the same garden several times : on the 19th 
of July humblebees were sucking the flowers in the 
proper manner, and none of the corollas were per- 
forated. On the 7th of August all the flowers were 
perforated, even those on some few plants of the 
salvia, which grew at a little distance from the great 



LOGICAL EXERCISES 325 

bed. On the 21st of August only a few flowers on 
the summits of the spikes of both species remained 
fresh, and not one of these was now bored. Again, 
in my own garden every plant in several rows of the 
common bean had many flowers perforated ; but I 
found three plants in separate parts of the garden 
which had sprung up accidentally, and these had not 
a single flower perforated. General Strachey for- 
merly saw many perforated flowers in a garden in 
the Himalaya, and he wrote to the owner to inquire 
whether this relation between the plants growing 
crowded and their perforation by bees there held 
good, and was answered in the affirmative. Hence 
it follows that the red clover and the common bean 
when cultivated in great masses in fields, Erica 
tetralix growing in large numbers on heaths, — rows 
of the scarlet kidney-bean in the kitchen garden, — 
and masses of any species in the flower garden are 
all eminently liable to be perforated. The explana- 
tion of this is not difficult. Flowers growing in 
large numbers attract crowds of insects. They are 
thus stimulated to work quickly by rivalry. Also 
many flowers have their nectaries dry, which is most 
quickly discovered by biting holes in them. — 
Charles Darwin. 

39. The seat of sensation is in the heart, as it is in 
the centre of the body; the brain is cold in order 
that it may counteract the heat of the heart. In or- 
der to temper the coldness of the brain, blood is con- 
veyed to the membrane which envelops it by means 
of veins or channels. But, lest the heat so conveyed 
should injure the brain, the veins, instead of being 



326 INDUCTIVE LOGIC 

large and few, are small and many, and the blood 
conveyed, instead of being copious and thick, is 
thin and pure. — Aristotle. 

40. The lungs of a fox must be a specific for 
asthma, because that animal is remarkable for its 
strong powers of respiration. — Paris' Pharmaco- 
logic,. 

41. Galileo discovered, by the use of his telescope, 
the four small satellites which circulate round Jupi- 
ter. It was then inferred that what happened on 
the smaller scale might also be found true of the 
larger planetary system. 

42. The first step toward the discovery of photog- 
raphy was the knowledge that visual light caused 
a chemical change in iodide of silver. The second 
step was to fix in permanent position the portion 
of the substance changed by the light, while the 
unchanged portion was removed. 

From what is known of the chemical elements 
and their compounds, it seems highly probable 
that numerous compounds may exist which are 
sensitive in the same way to waves of entirely 
different lengths from those that produce vision. 
Even with the salts of silver it has long been known 
that the range of wave-lengths capable of producing 
photographic effect is much greater than the visual 
range; and that the wave-lengths which produce 
the maximum physiological effect (light) are not 
the same as those that produce the maximum photo- 
graphic effect. 

It has been shown by Professor S. R. Langley 
that flint glass is transparent to waves about four 



LOGICAL EXERCISES 327 

times as long as the longest in the visual range ; 
and that rock-salt is transparent to a range below 
the red end of the visible spectrum twenty-nine 
times as long as the entire visual range. Glass is 
opaque to very short waves, its limit in that direc- 
tion being nearly coincident with the visual limit. 
Quartz, on the other hand, is transparent to a range 
of short waves extending far beyond the visual 
limit, but is opaque to very short waves. May not 
these substances prove valuable in this new field 
of actinography, as quartz trains have proved in 
photographing the ultra-violet spectrum ? 

Should the report of this discovery (Rontgen's) 
be confirmed, we cannot fail to accord the highest 
praise to this new triumph of science, and to pre- 
dict a development of the new field of actinography 
that may prove of greater importance than pho- 
tography. 

From the analogy between this form of radiant 
energy and dark heat it might appropriately be 
called « dark light." — The Electrical World, 

43. As to the theory of geyser-eruption, the 
following principles have been established. The 
boiling-point of water rises as the pressure in- 
creases, being 293° for a pressure of four atmos- 
pheres. Also, if the pressure be diminished when 
the water is under very strong pressure, the water 
will immediately flash into steam. Moreover, if 
the circulation is impeded, as when the water is 
contained in long, narrow, irregular tubes, and 
heated with great rapidity, the boiling-point will 
be reached below while it is far from this point in 



328 INDUCTIVE LOGIC 

the upper part of the tube. Therefore at the mo- 
ment of eruption, the boiling-point for the lowest 
depth is actually reached. The water there being 
transferred into steam, the expanding steam would 
lift the whole column of water in the tube, causing 
an overflow. This would diminish the pressure in 
every part of the tube, and consequently a large 
quantity of water before very near the boiling-point 
would flash into steam and instantly eject the 
whole of the water in the pipe, the steam rushing 
out immediately afterwards. The premonitory can- 
nonading beneath is evidently produced by the 
collapse of large steam-bubbles rising through the 
cooler part of the water of the tube. — Bunsen's 
Theory. 

44. Mackenzie's theory of geyser-eruption is 
that the geyser pipe is connected by a narrow con- 
duit with the lower part of a subterranean cave, 
whose walls are heated by the near vicinity of 
volcanic fires. The water rising above the opening 
of the conduit, and changing into steam, and having 
no way of escape, would, through pressure thus 
caused, be forced up the pipe, and the steam rushing 
after it. Professor Le Conte says of this theory : If 
there were but one geyser, this would be considered 
a very ingenious and probable hypothesis; for we 
may conceive of a cave and a conduit so constructed 
as to account for the phenomena. But there are so 
many geysers, that it is inconceivable that all of 
them should have caves and conduits so peculiarly 
constructed. This theory, therefore, is entirely un- 
tenable. 



LOGICAL EXERCISES 329 

45. It has been found by experiment that a 
current moving at the rate of three inches per 
second will take up and carry along fine clay ; 
moving six inches per second, will carry fine sand ; 
eight inches per second, coarse sand the size of lin- 
seed; twelve inches, gravel; twenty-four inches, 
pebbles ; three feet, angular stones of the size of a 
hen's egg. It will be readily seen that the carry- 
ing power increases much more rapidly than the 
velocity. For instance, a current of twelve inches 
per second carries gravel, while a current of three 
feet per second, only three times greater velocity, 
carries stones many hundred times as large as 
grains of gravel. 

46. If wood be soaked in a strong solution of 
sulphate of iron (copperas) and dried, and the same 
process be repeated until the wood is highly charged 
with this salt, and then burned, the structure of the 
wood will be preserved in the peroxide of iron left. 
Also, it is well known that the smallest fissures and 
cavities in rocks are speedily filled by infiltrating 
waters with mineral matters. Now, wood buried 
in soil soaked with some petrifying material becomes 
highly charged with the same, and the cells filled 
with infiltrated matter, and when the wood decays 
the petrifying material is left, retaining the struct- 
ure of the wood. In nature also there is an addi- 
tional process, not illustrated by the experiment, 
or by the example of infiltrated fillings. As each 
particle of organic matter passes away by decay, a 
particle of mineral matter takes its place, until 
finally the whole of the organic matter is replaced. 



330 INDUCTIVE LOGIC 

47. As to the origin of bitumen, the following 
observations have been made : Certain organic 
matters at ordinary temperature, in presence of 
abundant moisture, and out of contact of air, will 
undergo a species of decomposition or fermentation 
by which an oily or tarry substance, similar to bitu- 
men, is formed. In the interior of heaps of vegetable 
substance, such bituminous matter is often found. 
Fossil cavities have been found in solid limestone 
containing bitumen, evidently formed by decompo- 
sition of the animal matter. So, also, shales have 
been found in Scotland, filled with fishes which 
have changed into bitumen. 

48. Count Rumford in 1798 proved that the com- 
mon notion that heat was a substance was false, by 
boring a large piece of brass, under great pressure 
of the borer, whilst the brass was in a gallon of 
water; and at the end of two and one half hours 
the water actually boiled. 

49. Kenelm Digby's treatment of wounds was to 
apply an ointment, not to the wound itself, but to 
the sword that had inflicted it, to dress this care- 
fully at regular intervals, and in the meantime, 
having bound up the wound, to leave it alone for 
seven days. It was observed that many cures fol- 
lowed upon this treatment. 

50. When Pascal's barometer was carried to the 
top of Puy-de-D6me, and the mercury in it fell, it 
was inferred that the fall of the mercury was due 
to the change in elevation. Before finally accepting 
this conclusion, the barometer was placed in exposed 
positions and in sheltered, when the Avind blew and 



LOGICAL EXERCISES 331 

when it was calm, in rain and in fog; and these 
varying circumstances did not materially affect the 
result. 

51. A French experimenter, Pouchet, thought he 
had obtained indubitable evidence of spontaneous 
generation. He took infusions of vegetable matter, 
boiled them to a pitch sufficient to destroy all germs 
of life, and hermetically sealed the liquid in glass 
flasks. After an interval, micro-organisms appeared. 
It seems that at a certain stage in Pouchet's process, 
he had occasion to dip the mouths of the flasks in 
mercury. It occurred to Pasteur, in repeating the 
experiments, that germs might have found their 
way in from the atmospheric dust on the surface of 
this mercury. And when he carefully cleansed the 
surface of the mercury, no life appeared afterwards 
in his flasks. 

52. The causes to which the decay of the natives 
of New Zealand has been assigned are given as fol- 
lows : drink, disease, European clothing, peace, and 
wealth. — Journal of the Anthropological Institute. 

53. An eminent judge was in the habit of jocosely 
propounding, after dinner, a theory that the cause 
of the prevalence of Jacobinism was the practice 
of bearing three names. He quoted, on one side, 
Charles James Fox, Richard Brinsley Sheridan, 
John Home Tooke, John Philpot Curran, Samuel 
Taylor Coleridge, Theobald Wolfe Tone. On the 
other hand there were, William Pitt, John Scott, 
William Windham, Samuel Horsley, Henry Dun- 
das, Edmund Burke. Moreover, the practice of 
giving children three names has been a growing 



332 INDUCTIVE LOGIC 

practice, and Jacobinism has also been growing. 
The practice of giving children three names is more 
common in America than in England. In England, 
we still have a King and a House of Lords ; but the 
Americans are Republicans. Burke and Theobald 
Wolfe Tone are both Irishmen; therefore the be- 
ing an Irishman is not the cause of Jacobinism. 
Horsley and Home Tooke are both clergymen ; 
therefore the being a clergyman is not the cause of 
Jacobinism. Fox and Windham were both educated 
at Oxford ; therefore the being educated at Oxford 
is not the cause of Jacobinism. Pitt and Home 
Tooke were both educated at Cambridge ; therefore 
the being educated at Cambridge is not the cause of 
Jacobinism. The cause is, therefore, the having 
three names. — Macaulay. 

54. The exotic Pelargonia have a peculiar herring- 
bone structure in the petals ; moreover, the herring- 
bone structure is conjoined in the Pelargonia with 
the general characteristics of the Geraniese. Also 
the flowers with such seed-vessels as our wild gera- 
niums have the characters of Geranieae. It is, there- 
fore, exceedingly probable that our wild geraniums 
should have the peculiar herring-bone structure. 

55. Colonies ought not to rebel against the 
mother country, since they are its children and 
children ought not to rebel against their parents. 

56. Finding that the size of towns varies con- 
comitantly with the size of the rivers on which they 
are built, an observer might infer that the size of 
the river was due to the size of the town. 

57. An eminent author, writing on the work of 



LOGICAL EXERCISES 333 

the English Church before the Tractarian move- 
ment, contrasts the newer state of things unfavor- 
ably with the older, because the Church in those 
former days taught us to use religion as a light 
by which to see our way along the road of duty. 
Without the sun our eyes would be of no use to us ; 
but if we look at the sun, we are simply dazzled and 
can see neither it nor anything else. It is precisely 
the same with theological speculations. If the bea- 
con lamp is shining, a man of healthy mind will 
not discuss the composition of the flame. 

58. Scarlet color prevails among balsamina, 
Euphorbia, Pelargonium, poppy, Salvia, Bouvardia, 
and Verbena, yet none of the scarlets are of sweet 
perfumes. Some of the light-colored balsams and 
verbenas are sweet-scented, but none of the scarlets 
are. The common sage with blue blooms is odorif- 
erous both in flower and foliage; but the scarlet 
salvias are devoid of smell. None of the sweet- 
scented-leaved Pelargoniums have scarlet blooms, 
and none of the scarlet bloomers have sweet scent 
of leaves nor of blooms. Some of the white- 
margined poppies have pleasant odors; but the 
British scarlets are not sweet-scented. The British 
white-blooming hawthorn is of the most delightful 
fragrance; the scarlet flower has no smell. Some 
of the honeysuckles are sweetly perfumed, but the 
scarlet trumpet is scentless. 

59. The productive powers of plants, judging 
from the increased fertility of the parent-plants 
and from the increased powers of growth in the 
offspring, are favored by some degree of differ en- 



334 INDUCTIVE LOGIC 

tiation in the elements which interact and unite 
so as to form a new being. Here we have some 
analogy with chemical affinity or attraction, which 
comes into play only between atoms or molecules 
of a different nature. As Professor Miller re- 
marks : " Generally speaking, the greater the dif- 
ference in the properties of two bodies, the more 
intense is their tendency to mutual chemical action. 
But between bodies of a similar character the ten- 
dency to unite is feeble." 

60. In affirming that the growth of the body is 
mechanical, and that thought, as exercised by us, 
has its correlative in the physics of the brain, I 
think the position of the " materialist " is stated, as 
far as that position is a tenable one. I think the 
materialist will be able finally to maintain this po- 
sition against all attacks ; but I do not think, in 
the present condition of the human mind, that he 
can pass beyond this position. I do not think he is 
entitled to say that his molecular groupings and his 
molecular motions explain everything. In reality, 
they explain nothing. The utmost he can affirm is 
the association of the two classes of phenomena, of 
whose real bond of union he is in absolute ignorance. 
The problem of the connection of body and soul is as 
insoluble in its modern form as it was in the presci- 
entific ages. Phosphorus is known to enter into the 
composition of the human brain, and a trenchant 
German writer has exclaimed, "Ohne Phosphor, 
kein Gedanke ! " That may or may not be the case ; 
but even if we knew it to be the case, the knowledge 
would not lighten our darkness. — Tyndall. 



LOGICAL EXERCISES 335 

61. Granting that Hegel was more or less success- 
ful in constructing, a priori, the leading results of 
the moral sciences, still it was no proof of the correct- 
ness of the hypothesis of identity, with which he 
started. The facts of nature would have been the 
crucial test. That in the moral sciences traces of 
the activity of the human intellect and of the several 
stages of its development should present them- 
selves, was a matter of course ; but surely, if nature 
really reflected the result of the thought of a cre- 
ative mind, the system ought, without difficulty, to 
find a place for her comparatively simple phenomena 
and processes. — Helmholtz. 

62. When young Galileo was a student at Pisa, 
he noticed one day, during the service at the great 
Cathedral, the chandelier swinging backwards and 
forwards, and convinced himself, by counting his 
pulse, that the duration of the oscillations was 
independent of the arc through which it moved. 

63. Goethe enunciated the existence of a resem- 
blance between the different parts of one and the 
same organic being. According to Goethe's own 
account, the idea first occurred to him while looking 
at a fan-palm at Padua. He was struck by the im- 
mense variety of changes of form which the succes- 
sively developed stem-leaves exhibit, by the way in 
which the first simple root leaflets are replaced by 
a series of more and more divided leaves, till we 
come to the most complicated. He afterwards suc- 
ceeded in discovering the transformation of stem- 
leaves into sepals and petals, and of sepals and 
petals into stamens, nectaries, and ovaries, and thus 



336 INDUCTIVE LOGIC 

he was led to the doctrine of the metamorphosis of 
plants which he published in 1790. 

64. A fortunate glance at a broken sheep's-skull, 
which Goethe found by accident on the sand of the 
Lido at Venice, suggested to him that the skull it- 
self consisted of a series of very much altered verte- 
brae. At first sight no two things can be more un- 
like than the broad, uniform, cranial cavity of the 
mammalia, enclosed by smooth plates, and the nar- 
row cylindrical tube of the spinal marrow, composed 
of short, massy, jagged bones. — Helmholtz. 

65. The existence of the so-called blind spot in 
the eye was first demonstrated by theoretical argu- 
ments. While the long controversy whether the 
perception of light resided in the retina or the 
choroid was still undecided, Mariotte asked himself 
what perception there was where the choroid is 
deficient. He made experiments to discover this 
point and in the course of them discovered the 
blind spot. 

66. Hauy observed that crystals of "heavy spar" 
from Sicily and those from Derbyshire (which were 
considered to be the same substance) differed in their 
angles of cleavage by three and one-half degrees, and 
remarked: "I could not suppose that this difference 
was the effect of any law of decrement ; for it would 
have been necessary to suppose so rapid and complex 
a law, that such a hypothesis might have been justly 
regarded as an abuse of the theory." Vauquelin 
by chemical analysis discovered that the base of 
the crystals from Sicily was strontia, and that of 
those from Derbyshire was baryta. These facts, 



LOGICAL EXERCISES 337 

becoming known to Hai'iy, enabled him by inference 
to discover that the angles of crystals might be 
employed as a test for the presence of different 
substances which very nearly resemble each other 
in other respects. 

67. Graebe, a German chemist, in investigating 
a class of compounds, called the quinones, deter- 
mined incidentally the molecular structure of a 
body closely resembling alizarine, which had been 
discovered several years before. This body was 
derived from naphthaline, and, like many similar 
derivatives, was reduced back to naphthaline when 
heated with zinc-dust. This circumstance led the 
chemist to heat also madder alizarine with zinc- 
dust, when, to his surprise, he obtained anthracene. 
Of course, the inference was at once drawn that 
alizarine must have the same relation to anthracene 
that the allied coloring matter bore to naphtha- 
line; and, more than this, it was also inferred 
that the same chemical processes Avhich produced 
the coloring matter from naphthaline when applied 
to anthracene would yield alizarine. The result 
fully answered these expectations, and now ali- 
zarine is manufactured on a large scale from an- 
thracene obtained from coal-tar. — Cooke, The Neiv 
Chemistry. 

68. Sir Charles Lyell, by studying the fact that 
the river Ganges yearly conveys to the ocean as 
much earth as would form sixty of the great pyra- 
mids of Egypt, was enabled to infer that the ordi- 
nary slow causes now in operation upon the earth 
would account for the immense geological changes 



338 INDUCTIVE LOGIC 

that have occurred, without having recourse to the 
less reasonable theory of sudden catastrophes. 

69. Joule's experiments show that when heat is 
produced by the consumption of work, a definite 
quantity of work is required to produce that amount 
of heat which is known to the physicists as the unit 
of heat ; the heat, that is to say, which is necessary 
to raise one gramme of water through one degree 
centigrade. The quantity of work necessary for 
this is, according to Joule's best experiments, equal 
to the work which a gramme would perform in fall- 
ing through a height of 425 metres. 

In order to show how closely concordant are his 
numbers, I will adduce the results of a few series 
of experiments which he obtained after introduc- 
ing the latest improvements in his methods. 

(1) A series of experiments in which water was 
heated by friction in a brass vessel. In the interior 
of this vessel a vertical axle provided with sixteen 
paddles was rotated, the eddies thus produced being 
broken by a series of projecting barriers, in which 
parts were cut out large enough for the paddles to 
pass through. The value of the equivalent was 
424.9 metres. 

(2) Two similar experiments, in which mercury 
in an iron vessel was substituted for water in a 
brass one, gave 425 and 426.3 metres respectively. 

(3) Two series of experiments, in which a 
conical ring rubbed against another, both sur- 
rounded by mercury, gave 426.7 and 425.6 metres 
respectively. 

Exactly the same relations between heat and 



LOGICAL EXERCISES 339 

work Avere also found in the reverse process ; that 
is, when work was produced by heat. — Helmholtz. 

70. A gas which is allowed to expand with mod- 
erate velocity becomes cooled. Joule was the first 
to sIioav the reason of this cooling. For the gas has, 
in expanding, to overcome the resistance which the 
pressure of the atmosphere and the slowly yielding 
sides of the vessel oppose to it ; or, if it cannot of 
itself overcome this resistance, it supports the arm 
of the observer, which does it. Gas thus performs 
work, and this work is produced at the cost of its 
heat. Hence the cooling. If, on the contrary, the 
gas is suddenly allowed to issue into a perfectly ex- 
hausted space where it finds no resistance, it does 
not become cool, as Joule has shown. — Helmholtz. 

71. The principal feature in the plan of my at- 
tempt to penetrate into the North Polar region, or 
if possible to cross it, is, in brief, to try to make use 
of the currents of the sea, instead of fighting against 
them. My opinion is, as I have already explained 
on several occasions, that there must somewhere 
run currents into the Polar region, which carry the 
floe-ice across the Polar Sea, first northward toward 
the Pole, and then southward again into the Atlan- 
tic Ocean. That these currents really exist all 
Arctic expeditions prove, as most of them have had 
to fight against the currents and against the ice 
drifting southward, because they have tried to get 
northward from the wrong side. I think a very 
simple conclusion must be drawn from this fact that 
currents and drifting ice are constantly coming from 
the unknown north, viz. : Currents and perhaps also 



340 INDUCTIVE LOGIC 

ice must pass into this same region, as the water 
running out must be replaced by water running in. 
This conclusion is based upon the simplest of all 
natural laws ; but there seem to be people who will 
not even admit the necessity of this. 

That such currents run across the North Polar 
region is also proved by many facts. I may men- 
tion the great quantities of Siberian driftwood which 
are annually carried to the shores of Spitzbergen 
and Greenland; it comes in such abundance and 
with such regularity that it is quite impossible it 
should be carried to these shores, so far from the 
original home, by occasional winds or currents. 
There must be a regular communication between 
the coasts of Siberia and those of Spitzbergen and 
Greenland. By this same communication were 
several objects from the unfortunate Jeannette car- 
ried to the Greenland coast. The Jeannette sank 
in June, 1881, to the north of the New Siberian 
Islands, and three years afterward, in June, 1884, a 
great many objects belonging to her or her crew 
were found on an ice-floe on the southwest coast of 
Greetiland. This floe can only have been brought 
there by the same current which carries the drift- 
wood. By this same current an Esquimau imple- 
ment, a throwing-stick or harpoon-thrower, was also 
carried the long way from Alaska to the west coast 
of Greenland. There can, in my opinion, be no 
doubt of the existence of such a communication or 
current across the North Polar region from the 
Siberian side to the Greenland side. — Dr. Nansen 
in The Strand Magazine. 



INDEX 



Adams, 147. 

Adverbial probability, 232. 

Aggregates, Probability as af- 
fecting, 234 ff. 

Agreement, Method of, 84, 86 ff ., 
104, 128, 259, 275. 

Algebraical logic, 219. 

Analogy, 35, 39 ff., 44 ff., 202, 
204 ff., 283, 291. 

Analysis, (>0, 62, 186. 

Apperception, 3, 266. 

Aquapendente, 211. 

Arithmetical method, 37. 

Aristotle 16, 46, 50, 304. 

Association of ideas, 267. 

Astronomy, 284. 

Attention, 265. 

B. 

Bacon, Francis, 16, 46, 72, 73, 
94, 163, 199, 267, 269, 271, 275, 
276, 300, 303, 304, 309, 311. 

Bacon, Roger, 300. 

Bain, 16, 220. 

Barrett, 61, 264. 

Basis of probability, 232. 

Beneke, 36. 

Beudant, 141. 

Biology, 216, 284. 

Bluuts'chli, 294, 296. 

Boole, 219. 

Bosanquet, 7, 26. 27, 29, 40, 42, 
58, 81, 312. 



Botany, 283. 
Boyle, 104, 132. 
Bradley, 22. 
Brahe, Tycho, 76, 304. 
Brewster, 40, 97, 98. 
Brown, 59. 
Bullen, 247. 
Buusen, 150, 245. 



Caesalpinus, 304. 

Calculation of probability, 

2:'.0 ff. 
Campanella, 303. 
Causal analysis, 35, 40, 42, 45, 

47, 60, 64 ff. 
Causation. 45 ff., 47, 50 ff., 209, 

227, 228. 
Chalmers, 69. 
Chance, 240, 245 ff. 
Chemical combinations, 71. 
Chemistry, 288. 
Chenevix, 266. 

Circumstantial evidence, 247. 
Classification, 206 if., 279, 283. 
Clifford, 50, 164-166, 172, 218. 
Coexistence, 06, 92, 258. 
Coincidence, 245, 246. 
Collocation, 68. 69, 255, 256. 
Combinations, Theory of in 

causal analysis, 77 ff., 105. 
Concept, 90, 91, 205. 
Conceptual processes, Fallacies 

of, 263, 275 ff . 



341 



342 



INDEX 



Concomitant variations.Method 

of, 84, 85, 130 ft. 
Conservation of energy, 52 ff., 

71, 72, 288 ff. 
Consilience of inductions, 198. 
Content, explicit and implicit, 

6. 
Co-operative circumstances, 69. 
Copernicus, 304. 
Correlations, 67. 
Counteracting cause, 70. 
Counter-probability, 231. 
Cuvier, 9. 

D. 

Darwin, Charles, 68, 77, 113, 
123, 126, 139, 141, 154, 161, 175, 
181, 187, 213, 215, 218, 241. 

Darwin, G. H., 111. 

Davy, Sir Humphry, 149, 206, 
273. 

Deduction and induction, 16 ff., 
27. 

Deductive method, 147. 

DeMorgan, 74. 

Derivative laws, 253, 254. 

Descartes, 219. 

Development, 68, 218. 

Difference, Method of, 79, 84, 
85, 101 ff., 117, 149. 

Discovery, 202. 

Duhamel, 28. 



E. 

Elimination, 90. 

Ellis, 213. 

Empirical basis of probability, 

232. 
Empirical laws, 38, 252, 276. 
Enumeration, 43, 45 ft., 91, 

228 ff. 
Epistemology, 26, 58. 
Ethics, 295." 



Experiment, 10, 77 ff., 97, 176, 

282. 
Explanation, 14. 
Explanation, Historical, 291. 
Explicit content, 6 ff. 

F. 

Fact and truth, 19, 20. 
Fallacies, 262 ff . 
Faraday 61, 74, 112-114, 160, 
166, 169, 205, 217, 268, 273. 
Fictions, 196. 

Final cause. See Teleology. 
Florens, 223. 
Forel, 114. 
Franklin, Benjamin, 44. 

G. 

Galileo, 302, 304. 
Generalization, 23, 48, 49, 107, 

204, 205, 256 ff., 275 ff. 
Geology, 284 ff . 
Gide, 144, 241. 
Gilbert, 304. 
Glauber, 155. 
Gore, 167, 177, 206, 211, 264, 

266. 
Graber, 115. 
Green, 13, 45, 50, 58. 
Guyot, 97. 

H. 

Halley, 152, 159. 

Harvey, 211, 225. 

Hatchette, 141. 

Hegel, 294. 

Heraclitus, 270. 

Herschel, 59, 73, 149, 152, 217, 

275, 308 ff. 
Hippocrates, 223. 
Historical explanation, 291. 
Holland, 217. 
Hume, 4, 53-55. 
Huyghens, 158. 



INDEX 



343 



Hypothesis, 42, 93, 174 ff., 216, 

271 ff., 284, 308. 
Hypothetical universal, 31. 

I. 

Idols of Bacon, 269 ff. 
Imagination, 185, 202, 263, 271 ff. 
Implicit content, 6 ff. 
Increment of probability, 233, 

234. 
Induction and deduction, 16 ff. 
Inducto-deductive method, 156 

ff., 282. 
Inductive hazard, 24. 
Inference, 1 ff. 
Instances, Number of, 42. 
Insurance, 240. 
Intermixture of effects, 59. 
Invariability of causation, 51, 

54, 58. 
Inverse problem, 27. 



James, 10. 

Janet, 209, 210, 211, 224. 

Jenkin, 72, 164, 165. 

Jenner, 177, 222. 

Jevons, 27-29, 115, 143, 170, 

206-208, 217, 236, 246, 312. 
Joint method, 84, 85, 117 ff. 
Joule, 167. 
Judgment, Fallacies of, 263 

266 ff. 
Jurisprudence, 293 f. 

K. 

Kant, 53. 

Kepler, 76, 199, 304, 310. 
Kircher, 217. 
Kirchboff, 245. 

L. 

Ladd, 294. 
Laplace, 153, 179. 



Lavater, 18. 

Law, 30, 31. 

Leonardo da Vinci, 32, 301. 

Le Verrier, 147. 

Linnreus, 217. 

Lister, 219. 

Locke, 16, 307. 

Lockyer, 208. 

Lotze, 22, 25, 26, 29, 31, 46, 58, 

109, 188, 189, 312. 
Loua, 241. 
Lubbock, 83, 114, 120, 124 ff., 

195, 212, 213. 
Lyell, 138, 182. 

M. 

Malthus, 219, 256. 

Mansel, 57. 

Mathematical method, 172, 173. 

Mechanical combination, 70. 

Medicine, 99, 100. 

Mill, J. S., 16, 25, 30, 54-57, 59, 
68, 72, 79, 84, 86, 129, 156, 201, 
202, 220, 254, 260, 298, 309. 

Minto, 312. 

Molar forces, 71. 

Molecular forces, 71. 

N. 

Natural kinds, 67, 205, 206. 
Negation, Determination by, 

78 ff., 104. 
Negative conditions, 70. 
Newman, J. H., 312. 
Newton, 39, 153, 158, 159, 179,307. 
JVon causa pro causa, 267. 

O. 
Observation, 72 ff., 91, 227. 
Owen, 215. 

P. 

Pasteur, 98, 99, 160. 
Perception, 2 ff. 



344 



INDEX 



Perception, Fallacies of, 263 ff. 
Perfect induction, 3(5 ff. 
Physics, 282. 
Plateau, 115, 125. 
Plato, 50, 297. 
Plurality of causes, 59, 93. 
Political economy, 292 ff. 
Post hoc ergo propter hoc, 59, 

267. 
Postulate, Fundamental, 8, 26, 

189 ff., 261. 
Potential cause, 66, 108. 
Potential in inference, 11. 
Prediction, 156 ff. 
Presentation, Data of, 5. 
Preyer, 56. 
Priestley, 108. 

Probability, 29, 38, 43, 56, 226 ff . 
Proof, 202. 
Psychology and logic, 2 ff., 

14, 15, 47, 62, 133, 232, 262 ff., 

279, 289 ff . 
Psychology and history, 291 ff. 
Psychology, Method in, 294. 

Q. 

Quantitative determination, 72, 

131 ff., 282. 
Quetelet, 236. 

E. 

Railroad accidents, 236 ff. 
Reality, Inference an indirect 

reference to, 13. 
Reduction, 28, 42. 
Residues, 84, 85, 146 ff. 
Ricardo, 132. 
Romanes, 200. 
Rule, 30. 



Saigey, 89, 135. 
Saint-Pierre, 224. 
Schleiermacher, 16. 



Schwann, 219. 

Science, 33. 

Sciences and the inductive 

method, 281 ff. 
Scientific analysis. See Causal 

analysis. 
Scientific spirit, 33, 164, 201. 
Sequence, 64 ff., 92. 
Sidgwick, 268. 
Sigwart, 26, 29, 57, 58, 68, 94, 

107, 202, 312. 
Similarity, Law of, 205. 
Smith, Adam, 268. 
Socrates, 297. 
Spencer, 257, 284-286. 
Spinoza, 187. 
Sprengel, 213. 
Sufficient reason, 58. 
Suggestion of causal relation, 

99, 224. 
Synthesis, 186. 
System, 7 ff., 12, 17 ff., 44, 45, 

58, 148, 176, 209, 211, 266. 



Tait, 52, 133, 151, 153, 159, 168, 

177, 180, 197. 
Teleology, 208 ff., 222 ff., 278. 
Telesius, 302. 
Tennyson, 12, 51. 
Thomson, 133, 151, 153. 
Totality, Law of, 7. 
Truth and fact, 19, 20. 
Tyndall, 75, 76, 80, 81, 102, 135, 

166, 183, 185, 217. 



U. 
Ueberweg, 32, 43, 58, 274, 300. 
Ultimate laws, 253, 254. 
Uniformity of nature, 22, 25, 

51, 54 ff. 
Universal, 12, 18, 275. 
Universal causation, 51. 



INDEX 



345 



V. 

Venn, 29, 57, 77, 10G, 111, 180, 

260, 312. 
Verification, 15(5 ff. 
Voltaire, 223. 

W. 
Waitmann, 205. 
Wallace, 191. 



Weber's law, 72, 143. 

Whately, 57, 311. 

Whewell, 30, 198, 201, 202, 273, 

301, 302, 310. 
Wollaston, 26(5. 



Zoology, 283. 



Sx 



